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By the Authority Vested By Part 5 of the United States Code § 552(a) and 
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HEED THIS NOTICE : Criminal penalties may apply for noncompliance. 




Document Name: CIE 15: Technical Report: Colorimetry, 3rd edition 



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Standards Body: international Commission on Illumination 




ISBN 3 901 906 33 9 



COMMISSION INTERNATIONALE DE L'ECLAIRAGE 
INTERNATIONAL COMMISSION ON ILLUMINATION 
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Y 



CIE 15:2004 
3rd Edition 



UDC: 



535.66 
535.67 
612.843.31 
159.937.51 



Descri ptor : Coiori metry 

Colour of objects 
Colour vision 
Perception of colour 



CIE 15:2004 



This Technical Report has been prepared by CiE Technical Committee 1-48 of Division 1 
"Vision and Colour" and has been approved by the Board of Administration of the 
Commission Internationale de I'Eclairage for study and application. The document reports on 
current knowledge and experience within the specific field of light and lighting described, and 
is intended to be used by the CIE membership and other interested parties. It should be 
noted, however, that the status of this document is advisory and not mandatory. The latest 
CIE proceedings or CIE NEWS should be consulted regarding possible subsequent 
amendments. 



Ce rapport technique a ete elabore par le Comite Technique CIE 1-48 de la Division 1 "Vision 
et Couleur" et a ete approuve par le Bureau de la Commission Internationale de I'Eclairage, 
pour etude et emploi. Le document expose les connaissances et I'experience actuelles dans 
ie domaine particulier de la lumiere et de I'eclairage decrit ici. II est destine a etre utilise par 
les membres de la CIE et par tout les interesses. II faut cependant noter que ce document est 
indicatif et non obiigatoire. II faut consulter les plus recents comptes rendus de la CIE, ou le 
CIE NEWS, en ce qui concerne des amendements nouveaux eventuels. 



Dieser Technische Bericht ist vom CIE Technischen Komitee 1-48 der Division 1 "Sehen und 
Farbe" ausgearbeitet und vom Vorstand der Commission Internationale de I'Eclairage gebilligt 
worden. Das Dokument berichtet uber den derzeitigen Stand des Wissens und Erfahrung in 
dem behandelten Gebiet von Licht und Beleuchtung; es ist zur Verwendung durch CIE- 
Mitglieder und durch andere Interessierte bestimmt. Es sollte jedoch beachtet werden, daB 
das Dokument eine Empfehlung und keine Vorschrift ist. Die neuesten CIE-Tagungsberichte 
Oder das CIE NEWS sollten im Hinblick auf mogliche spatere Anderungen zu Rate gezogen 
werden. 



Any mention of organisations or products does not imply endorsement by the CIE. Whilst 
every care has been taken in the compilation of any lists, up to the time of going to press, 
these may not be comprehensive. 



Toute mention d'organisme ou de produit n'implique pas une preference de la CIE. Maigre le 
soin apporte a la compilation de tous les documents jusqu'a la mise sous presse, ce travail 
ne saurait etre exhaustif. 



Die Erwahnung von Organisationen oder Erzeugnissen bedeutet keine Billigung durch die 
CIE. Obgleich grofte Sorgfalt bei der Erstellung von Verzeichnissen bis zum Zeitpunkt der 
Drucklegung angewendet wurde, ist es moglich, daft diese nicht vollstandig sind. 



© CIE 2004 - All rights reserved 



CIE 15:2004 



This report has been prepared by the Technical Committee 1-48 "Revision of CIE document 
15.2 Colorimetry" of CIE Division 1 "Colour and Vision" by using previously published material 
of the CIE and considering resolutions of the CIE Division 1 meeting at Teddington 2000-04- 
06 and Rochester 2001-06-22/23. This present publication replaces CIE 15.2-1986 
"Colorimetry"', 



Members of the Technical Committee during the preparation of this report were: 



P J. Alessi 


USA 


EC. Carter 


USA 


M.D. Fairchild 


USA 


R.W.G. Hunt 


United Kingdom 


C.S. McCamy 


USA 


B. Kranicz 


Hungary 


J.R. Moore 


United Kingdom 


L. Morren 


Belgium 


J.H. Nobbs 


United Kingdom 


Y. Ohno 


USA 


M.R. Pointer 


United Kingdom 


D.C. Rich 


USA 


A.R. Robertson 


Canada 


J.D. Schanda (chair) 


Hungary 


R. Seve 


France 


P.W. Trezona 


United Kingdom 


K.Witt 


Germany 


H. Yaguchi 


Japan 



The following Editorial Committee was responsible for the formulation of the document: E.C. 
Carter, Y. Ohno, M.R. Pointer, A.R. Robertson, R. Seve, J.D. Schanda, K. Witt. 



Items of mainly historic importance have been placed into Appendix A. 



According to the new CIE publication numbering policy - that indicates a new revised edition 
only by the year of publication - this technical report has got the number of 15:2004 and not 
15.3:2004. 



Ill 



CIE 15:2004 



TABLE OF CONTENTS 

SUMMARY VII 

RESUME VII 

ZUSAMMENFASSUNG VII 

1. SCOPE 1 

2. PREFACE 1 

3. RECOMMENDATIONS CONCERNING STANDARD PHYSICAL DATA OF 
ILLUMINANTS AND SOURCES 2 

3.1 Recommendations concerning standard physical data of illuminants 2 

3.2 Artificial sources representative of illuminants 5 

4. RECOMMENDATIONS CONCERNING STANDARD OF REFLECTANCE 5 

5. RECOMMENDATIONS CONCERNING GEOMETRIC CONDITIONS FOR 
COLORIMETRY 5 

5.1 Recommended nomenclature for directional irradiation 6 

5.1.1 Forty-five degree directional geometry (45°x) 6 

5.1.2 Forty-five degree annular geometry (45°a) 6 

5.1.3 Zero degree directional geometry (0°) 6 

5. 1 .4 Eight degree geometry (8°) 7 

5.2 Recommended geometry for reflection measurements 7 

5.2.1 Diffuse: eight-degree geometry, specular component included (di:8°) 7 

5.2.2 Diffuse: eight-degree geometry, specular component excluded (de:8°) 7 

5.2.3 Eight degree: diffuse geometry, specular component included (8°:di) 7 

5.2.4 Eight degree: diffuse geometry, specular component excluded (8°:de) 7 

5.2.5 Diffuse /diffuse geometry (d:d) 7 

5.2.6 Alternative diffuse geometry (d:0°) 7 

5.2.7 Forty-five degree annular / normal geometry (45°a:0°) 7 

5.2.8 Normal / forty-five degree annular geometry (0°:45°a) 8 

5.2.9 Forty-five degree directional / normal geometry (45°x:0°) 8 

5.2.10 Normal / forty-five degree directional geometry (0°:45°x) 8 

5.3 Recommended geometry for transmission measurements 8 

5.3.1 Normal / normal geometry (0°:0°) 8 

5.3.2 Diffuse / normal geometry, regular component included (di:0°) 9 

5.3.3 Diffuse / normal geometry, regular component excluded (de:0°) 9 

5.3.4 Normal / diffuse geometry, regular component included (0°:di) 9 

5.3.5 Normal / diffuse geometry, regular component excluded (0°:de) 9 

5.3.6 Diffuse / diffuse geometry (d:d) 9 

6. RECOMMENDATIONS CONCERNING STANDARD OBSERVER DATA 9 

6.1 CIE 1931 standard coiorimetric observer 9 

6.2 CIE 1964 standard coiorimetric observer 10 

7. RECOMMENDATIONS CONCERNING THE CALCULATION OF TRISTIMULUS 
VALUES AND CHROMATICITY COORDINATES 12 

7.1 Calculation of tristimulus values 12 

7.1.1 Secondary light sources (reflecting or transmitting objects) 1 2 

7.1.2 Illuminants and self-luminous objects 13 

7.2 The use of abridged or truncated data 1 3 

7.2.1 Abridgement 13 

7.2.2 Truncation 14 

7.2.3 Weighting factors 14 

7.2.4 Numerical procedures 15 

7.2.5 Bandwidth of a spectrometer 15 

7.3 Calculation of chrornaticity coordinates 15 

7.4 Equations representing relationships between colour stimuli 16 



IV 



CIE 15:2004 



8. RECOMMENDATIONS CONCERNING UNIFORM COLOUR SPACING AND 

COLOUR DIFFERENCES 16 

8.1 CIE 1976 uniform chromaticity scale diagram (UCS diagram) 16 

8.2 CIE 1976 uniform colour spaces 16 

8.2.1 CIE 1976 (L*a*b*) colour space; CIELAB colour space 17 

8.2.2 CIE 1976 (L*u*v*) colour space; CiELUV colour space 18 

8.2.3 Notes on CIE 1976 uniform colour spaces 19 

8.3 Improved industrial colour difference evaluation 20 
8.3.1 C1EDE2000 total colour difference formula 20 

9 RECOMMENDATIONS CONCERNING MISCELLANEOUS COLORIMETRIC 

PRACTICES AND FORMULAE 22 

9.1 Dominant wavelength and purity 22 

9.1.1 Dominant wavelength (of a colour stimulus), X d 22 

9.1.2 Complementary wavelength (of a colour stimulus), X c 22 

9.1.3 Colorimetric purity, p c 22 

9.1.4 Excitation purity, p e 22 

9.2 Special metamerism indices 23 

9.2.1 Special metamerism index: change in illuminant 23 

9.2.2 Special metamerism index: change in observer 24 

9.3 Assessment of the quality of a daylight simulator for colorimetry 25 

9.4 The evaluation of whiteness 26 

9.5 Calculation of correlated colour temperature 26 

10. REFERENCES 27 

11. TABLES 30 
11.1 Table T.1. Relative spectral power distributions of CIE illuminants 30 
11. 2 Table T.2. Components S (2), Si(A), S^X) 33 
1 1.3 Table T. 3. Tristimulus values, chromaticity coordinates of CIE illuminants 35 
11.4TableT.4. CIE 1931 standard colorimetric observer 36 
11.5TableT.5. CIE 1964 standard colorimetric observer 38 
1 1 .6 Table T.6. Relative spectral power distributions of illuminants representing typical 

fluorescent lamps, for wavelengths X = 380 nm to 780 nm at 5 nm intervals 40 

11.7 Table T.7. High pressure discharge lamps. HP1: Standard high pressure sodium 
lamp; HP2: Colour enhanced high pressure sodium lamp; HP3-5: Three types of 
high pressure metai halide lamps 47 

11.8 Table T.8. Colorimetric data for the fluorescent lamp illuminants of Table T.6 49 

1 1.9 Table T.9. Colorimetric data for the high pressure illuminants of Table T.7 50 

1 1 .10 Table T.10. Values of the first deviation function used in the calculation of the 
observer metamerism index 51 

APPENDIX A. OLD RECOMMENDATIONS, NOW OBSOLETE, AS WELL AS 

REFERENCES TO NON-CIE COLOUR DIFFERENCE FORMULAE 52 

Appendix A. 1 . Illuminant B and Source B 52 

Appendix A.2. Illuminant C and Source C 52 

Appendix A.3. CIE 1964 uniform colour space and colour difference formula 53 

u, v uniform chromaticity scale (CIE 1960 UCS) diagram 53 

1964 uniform space and colour difference formula 53 

Appendix A.4. CIE 1994 colour difference formula (CIE94) 53 

Appendix A.5. CMC(i:c) colour difference formula 54 

Appendix A. 6. DIN99 colour difference formula 54 

References 54 

APPENDIX B. DEFINITIONS OF THE 7(X\g(X)MX) COLOUR-MATCHING 

FUNCTIONS, THE CIE RGB SYSTEM AND THE DERIVATION OF THE CIE XYZ 
SYSTEM FROM THE CIE RGB SYSTEM FOR THE 1931 STANDARD OBSERVER 55 

Appendix B.1. Determination of the r{X) 1 g(X),b(X) colour-matching functions 55 

Appendix B.2. Derivation of the CIE XYZ trichromatic system from the CIE RGB 

trichromatic system 56 



V 



CIE 15:2004 



Appendix B.3. Definition of the colour-matching functions in the CIE 1964 trichromatic 

system 57 

Reference 61 

APPENDIX C. ALTERNATIVE METHOD TO DEFINE DAYLIGHT ILLUMINANTS - 
METHOD OF CALCULATION, CORRECTED TABLES AND EQUATIONS (FOR 
INFORMATION AND EVALUATION) 62 

References 65 

APPENDIX D. REVERSE TRANSFORMATION FROM VALUES L*. a*, b* TO 

TRISTIMULUS VALUES X, Y, Z 66 

Reference 66 

APPENDIX E. INFORMATION ON THE USE OF PLANCK'S EQUATION FOR 

STANDARD AIR 67 

References 67 

EXPLANATORY COMMENTS 68 



Vi 



CI E 15:2004 



COLORIMETRY 

SUMMARY 

This publication provides the recommendations of the CIE concerning basic coiorimetry. 
Specifically, it includes the use of the standard illuminants and the standard colorimetric 
observers; the reference standard for reflectance; the illuminating and viewing conditions; the 
calculation of tristimulus values, chromaticity coordinates, colour spaces and colour 
differences; and the various other colorimetric practices and formulae. 

This publication is consistent with the fundamental data and procedures described in 
the CIE Standards on Coiorimetry. 

For further details of some of the phenomena discussed here the reader is directed to 
the appropriate technica! reports. 



COLORIMETRIE 

RESUME 

Ce document donne ies recommandations de la CIE pour la colorimetrie de base. Plus 
particulierement il traite de I'emploi des illuminants normalises et des observateurs 
colorimetriques normalises, de la reference normaiisee pour le facteur de reflexion, des 
conditions d'eclairage et d'observation, du calcul des composantes trichromatiques, des 
coordonnees trichromatiques, des espaces chromatiques et des ecarts de couleur, ainsi que 
de i'emploi de diverses autres pratiques et formules colorimetriques. 

Cette publication est en accord avec ies donnees et procedures de base qui sont 
decrites dans Ies normes CIE de colorimetrie. 

Pour des details complementaires relatifs aux questions traitees ici, le lecteur est 
invite a consulter Ies rapports techniques appropries. 



FARBMESSUNG 

ZUSAMMENFASSUNG 

Die hier wiedergegebenen Empfehlungen der CIE beziehen sich auf die Anwendung Oder die 
Benutzung der Normlichtarten und der Normalbeobachter, auf den WeiGstandard, auf die 
Beleuchtungs- und Beobachtungsbedingungen, auf die Berechnung von Normfarbwerten und 
Normfarbwertanteilen, FarbenrSumen und Farbabstanden, und auf verschiedene andere 
farbmetrische Praktiken und Formeln. 

Diese Veroffentlichung stimmt mit den grundlegenden Daten und Verfahren uberein, 
die in CIE Normen fur Farbmessung beschrieben sind. 

Weitere Einzelheiten einiger hier dsskutierter Phanomene findet der Leser in 
geeigneten technischen Berichten. 



VII 



C!E 15:2004 



VIII 



CiE 15:2004 



1. SCOPE 

This report is intended to provide a consistent and comprehensive account of the 
recommendations of the CIE for basic colorimetry. It summarises basic colorimetric data and 
practices; it does not, however, deal with colour appearance specification. 

2. PREFACE 

By general consent in all countries the specification of basic standards for use in colorimetry 
is the province of the Commission Internationale de I'Eclairage (CIE). The first major 
recommendations regarding colorimetric standards were made by the CIE in 1931, and these 
formed the basis of modern colorimetry. The original recommendations of 1931 were 
reviewed from time to time by the CIE Colorimetry Committee and later by CIE Division 1, 
Vision and Colour When necessary changes were made. New recommendations were 
added to supplement the existing ones or to broaden the scope of colorimetry in accordance 
with developments in practice and science. 

The deliberations and recommendations made by the CIE Colorimetry Committee 
and Division 1 are recorded in the Proceedings of the various Sessions of the CIE. However 
the access to these Proceedings has always been rather limited and much of the material 
published in the Proceedings is obsolete or inconsistent with current colorimetric practice. 
The recommendations, while few in number, also present an incoherent picture. Many 
recommendations are merely proposals of study or work on certain topics that were 
considered important at the time. 

For these reasons in 1971 the CIE published a special document on colorimetry to 
provide a consistent and comprehensive account of basic colorimetric recommendations. 
This document was not intended to be a textbook on colorimetry but rather a reference to the 
basic standards that govern modern colorimetry. The document was issued as CIE 
Publication No. 15 (CIE, 1971). 

Since 1971 it has been necessary to add two supplements to the document [Suppl. 1 
on Special metamerism index: change of iliuminant (CIE, 1972) and Suppl. 2 on 
Recommendations on uniform colour spaces, colour-difference equations and psychometric 
colour terms (CIE, 1978)]. Several Technical Reports were also published during the 
intervening years. Publication CIE 15.2, published in 1986 (CIE, 1986b) incorporated the first 
two supplements. Further amendments, described in detail in CIE 51-1981, A method for 
assessing the quality of daylight simulators for colorimetry (CIE, 1981); CIE 80-1989, Special 
metamerism index: observer metamerism (CIE, 1989); CIE 101-1993, Parametric effects in 
colour difference evaluation (CIE, 1993); CiE 116-1995, Industrial colour difference evaluation 
(CIE, 1995a); CiE 135/3, CIE TC 1-45 report: Supplement 1-1999 to CIE 51-1981, Virtual 
metamers for assessing the quality of simulators of CIE iliuminant D50 (CIE, 1999b) and CIE 
142-2001 , Improvement to industrial colour difference evaluation (CIE, 2001a) are all parts of 
the CiE system of colorimetry. The present version, CIE 15:2004 summarises all CIE 
recommendations on basic colorimetry. Short explanatory texts and a historic overview are 
also included. Colour appearance models are not covered, for these see CiE 131-1998 (CIE, 
1998a); CIE 159:2004 (CIE, 2004b) and CIE X014-1998 (CIE, 1998b). 

In compiling this third edition the opportunity has been taken to incorporate all 
relevant recommendations. The publications enumerated in the previous paragraph contain 
background information on the single subjects, those interested in more detail about the 
development of the recommendations and their background experiments are referred to these 
publications. CIE 15:2004 is based on CIE standards containing the fundamental data on CIE 
standard illuminants and standard observers. The presently official versions of these 
standards are CIE S 005-1998, CIE standard illuminants for colorimetry (CIE, 1998c) 
(published also as ISO 10526:1999) and CIE S 002-1986, CIE standard colorimetric 
observers (CIE, 1986a), (published also as CIE/ISO 10527:1991). These standards contain 
the fundamental colorimetric data [see also CIE DS 014-2.2:2004 (CIE, 2004a)]. 

It is anticipated that further amendments of colorimetric practice and further 
standards will be published, thus one should consult the latest CIE list of publications 
published in CIE Proceedings, and in most recent Technical Reports; this information is also 
available on the CIE world wide web home page (http://www.cie.co.at/). 



CIE 15:2004 



The wording of the original recommendations has been altered to be consistent with 
modern nomenclature and in some cases the original recommendations have also been 
modified in content to bring them into line with present day thinking and practice. The 
versions given in this document are the recommendations now in force and supersede all 
previous recommendations until such time as any amendments are published by the CIE. 

The recommendations are divided into the following seven groups: 

- Recommendations concerning standard physical data of illuminants and sources. 

- Recommendations concerning the standard of reflectance. 

- Recommendations concerning geometric conditions for colorimetry. 

- Recommendations concerning standard observer data. 

- Recommendations concerning the calculation of tristimulus values and chromaticity 
coordinates. 

- Recommendations concerning uniform colour spacing and colour difference. 

- Recommendations concerning miscellaneous colorimetric practices and formulae. 

The definitive data relating to standard colorimetric illuminants and observers are 
those given at 1 nm intervals in the appropriate CIE standards [CIE, 1998c (to be replaced by 
CIE, 2004a); CIE, 1986a]. The data have not been printed in the present report, but are 
included in the accompanying CD-ROM. Abridged data, at 5 nm intervals, are given in 
Section 11, and these may be used in those cases where calculation at the wider intervals is 
unlikely to produce any significant error. 

For ali colorimetric calculations wavelength in standard air should be used l! \ 



3. RECOMMENDATIONS CONCERNING STANDARD PHYSICAL DATA OF 

ILLUMINANTS AND SOURCES 

3.1 Recommendations concerning standard physical data of illuminants 2 

It is recommended that the following illuminants, defined by relative spectral power 
distributions given in Table 1 of CIE S 005-1998 (CIE, 1998c) m , be used for general 
colorimetry. 

• CIE standard illuminant A 

The relative spectral power distribution S A (A) is defined by the equation 

1,435x10 7 A 
ex p 1 



jfSGOY '2848x560 



S A (2) = 100 — x 7 (3-1) 

A { A J 1,435x10 7 „ 

exp 1 

2 848/1 

where A is the wavelength in nanometres and the numerical values in the two exponential 
terms are definitive constants originating from the first definition of Illuminant A in 1931 3 . This 
spectral power distribution is normalized to the value 100 (exactly) at the wavelength 560 nm 
(exactly). 

CIE standard illuminant A is defined over the spectral region from 300 nm to 830 nm iV 
in CIE S 005-1998 (CIE, 1998c) to six significant digits. Should higher precision be needed, 



!t Superscripts of Arabic numerals refer to Explanatory Comments given on page 68-72. 

! " The spectral power distribution tables published in the CIE Standard are reproduced on the 
CD-ROM that accompanies this Technical Report. 

!V The wavelength range for standard illuminants is 300 nm - 830 nm because, for evaluating 
luminescent samples the UV spectral range is relevant. For most colorimetric investigations 
the restricted wavelength range, 380 nm - 780 nm, can be used. 



CI E 15:2004 



values calculated using Equ 3.1 should be used v Section 11 contains abridged tables that 
can be used in most practical calculations. On the use of these tables see Section 7.2. 

Note 1: The definition reproduced here is in accordance with the values of iliuminant A 
originally published in 1931, see CIE S 005-1998 (CIE, 1998c) and CIE DS014- 
2.2:2004 (CIE, 2004a). 

Note 2: Despite the fact that Equ. 3.1 is based on Planck's equation for a vacuum, the 
wavelengths are to be taken as being in standard air (dry air at 15°C and 101325 Pa, 
containing 0,03% by volume of carbon dioxide). This makes CIE standard iliuminant A 
compatible with other CIE colorimetric and photometric data. 

« CIE standard iliuminant D65 

The relative spectral power distribution representing a phase of daylight with a correlated 
colour temperature of approximately 6500 K (called also nominal correlated colour 
temperature of the daylight iliuminant) 4 , symbol: S D65 (i). The official values of S D65 (/i) are as 
given in CIE standard illuminants for colorimetry (CIE, 1998c) vl . 

Note 1: Regarding the definition of correlated colour temperature (T" cp ) of an iliuminant see 
Section 9.5. 

Note 2: Section 11 provides abridged tables that can be used in many practical calculations. 
On the use of these tables see Section 7.2. The values of relative spectral power 
distribution of CIE standard iliuminant D65 given in Table T.1 at 5 nm intervals are 
consistent with the values from 300 nm to 830 nm at 1 nm intervals and with six 
significant figures given in CIE standard illuminants for colorimetry (CIE, 1998c). They 
have been taken from the tables of the Standard. 

Note 3: If values at other wavelengths than printed in Table 1 of the standard (CIE, 1998c) at 
1 nm intervals are needed, linear interpolation should be used. 

• Other illuminants D 

It is recommended that, in the interest of standardization, D65 be used whenever possible. 
When D65 cannot be used, it is recommended that one of the daylight illuminants D50, D55, 
or D75 defined in Table T.1 be used. When none of these daylight illuminants can be used, a 
daylight iliuminant at a nominal correlated colour temperature (T cp ) can be calculated using 
the following equations. These equations will give an iliuminant whose correlated colour 
temperature is approximately equal to the nominal value, but not exactly so 4 . 

(a) Chromaticity 

The 1931 (x,y) chromaticity coordinates of the daylight (D) to be defined must satisfy the 
following relation: 

y D = -3,000x D 2 + 2 t 870x D - 0,275 (3.2) 

with x D being within the range of 0,250 to 0,380. The correlated colour temperature 7 cp of 
daylight D is related to x D by the following formulae based on normals to the Planckian locus 
on a uniform chromaticity diagram (see Section 9.5): 

(i) for correlated colour temperatures from approximately 4000 K to 7000 K: 
-4,6070x10 9 2,9678x10 6 0,09911x10 3 nr%AAnnrt 

Xo ' u f "s cr* 0244061 (3 - 3) 

(ii) for correlated colour temperatures from greater than 7000 K to approximately 25 000 K: 



v Terminology in this publication follows the traditional terminology used in colorimetry. A 
separate publication on colorimetry will deal with the current "uncertainty" description of 
stating measurement results and will recommend methods for calculating colorimetric 
uncertainties. 

Vl The spectral power distribution tables published in the CIE Standard are reproduced on the 
CD-ROM that accompanies this Technical Report. 



CIE 15:2004 

-2,0064x10 9 1,9018x10 6 0,24748x10 3 n ^ nAn ,_ 

x °=^j — u — ^ +w3?o4 ° <34 » 

(b) Relative spectral power distribution 

The relative spectral power distribution S(A) of daylight D is to be computed from 

S(Xj = S (A) + M,S,(A) + M 2 S 2 (1) (3.5) 

where S (A), S^Xj, S Z U) are functions of wavelength, A, given in Table T.2, and M u M 2 are 
factors whose values are related to the chromaticity coordinates x Dl y D as follows: 

M - " 1 . 3515 -V 703x d +5,9114y D 
1 ~ 0,0241 + 0,256 2x D - 0,734 1y D 

(3.6) 
_ 0,0300 -31,44 24x D +30,0717y D 



0,024 1 + 0,256 2x D - 0,734 1y D 

Notes on standard illuminant D65 and other illuminants D 

Note 1: Seasonal and geographical variations in the spectral power distribution of daylight 
occur, particularly in the ultraviolet spectral region, but this recommendation should 
be used pending the availability of further information on these variations. 

Note 2: The spectral power distributions of daylight illuminants D produced by this 
recommendation are based on experimental observations over the wavelength range 
330 nm to 700 nm, and on extrapolation in the wavelength ranges 300 nm to 330 nm 
and 700 nm to 830 nm (see Judd et al., 1964). The extrapolated values are believed 
to be accurate enough for colorimetric purposes, but should not be used for other 
purposes. 

Note 3: If values at other wavelengths than those printed in Table T.2 are needed, linear 
interpolation should be used (see also Appendix C). 

Note 4: The relative spectral power distributions of the D illuminants given in Table T.1 and in 
the CIE standard on illuminants for colorimetry (CIE, 1998c) were derived by the 
procedure given above with some intermediate rounding and with some adjustments 
for changes in the International Temperature Scale 5 . Thus for historic reasons, the 
tabulated values are slightly different from the calculated values. For the time being 
the tabulated values are the official data. (Eventually these data may be superseded 
by the method described in Appendix C, which provides a harmonised method of 
calculation for trial that will produce congruent results if the modified tables and 
equations are used.) 

Note 5: When samples exhibiting luminescence excited by ultraviolet radiation are involved, 
one of the D illuminants defined in these recommendations should always be used to 
represent daylight. 

« Illuminant B 

Intended to represent direct sunlight with a correlated colour temperature of approximately 
4900 K. 

Note: The use of this illuminant is deprecated, see Appendix A. 

9 Illuminant C 

Intended to represent average daylight with a correlated colour temperature of approximately 
6800 K. 

Note 1 : Illuminant C does not have the status of a CIE standard but its relative spectral power 
distribution, tristimulus values and chromaticity coordinates are given in Table T.1 
and Table T.3, as many practical measurement instruments and calculations still use 
this illuminant. 

Note 2: The tristimulus values and chromaticity coordinates of the illuminant C and of D50, 



CI E 15:2004 



D55, D75, calculated from the values of S(A), given in Table T.2., are shown in Table 
T.3. The reproduced tristimulus values are those of the perfect reflecting diffuser 
irradiated by the respective illuminant, see Section 7.1.1 This table also includes 
similar data for C1E standard illuminant A and D65. 

3.2 Artificial sources representative of illuminants 

It is recommended that the following artificial sources be used if it is desired to realise the 
illuminants defined in Section 3.1 for actual laboratory inspection. 

• Source A 

CIE standard illuminant A is to be realised by a gas-filled tungsten filament lamp operating at 
a correlated colour temperature of 2856 K (c 2 = 1, 4388x1 0' 2 m-K). If the source is also to be 
used in the UV region, a lamp having an envelope or window made of fused-quartz or silica 
must be used because glass absorbs the UV component of the radiation from the filament, 

• Source B 

See Appendix A. 

• Source C 

See Appendix A. 

o Source D65 

At present no artificial source is recommended to realise CIE standard illuminant D65 or any 
other illuminant D of different correlated colour temperature. It is hoped that new 
developments in light sources and filters will eventually offer sufficient basis for a CIE 
recommendation. Meanwhile the CIE has agreed on a formula to describe the quality of a 
daylight simulator for colorimetry, see Section 9.3. 

Notes on artificial sources representative of illuminants 

Note 1: The artificial sources defined above and recommended as representative sources for 
CIE illuminants are named "CIE sources for coiorimetry". 

Note 2: Whenever the highest accuracy of the spectral power distribution of a standard is 
required, it is advisable to make a spectroradiometric calibration of the actual source 
used, because the relative spectral power distribution of the source may not exactly 
coincide at all wavelengths with that defining the corresponding illuminant. 

Note 3: The spectrum of a D65 simulator fluorescent lamp is reproduced in Table T.6.2b as 
FL3.15, see Section 9.3. 



4. RECOMMENDATIONS CONCERNING STANDARD OF REFLECTANCE 6 

The perfect reflecting diffuser is the reference standard for reflectance (CIE, 1986a). It is 
defined as the ideal isotropic diffuser with a reflectance equal to unity. For real 
measurements, reflectance standards, such as pressed barium sulphate or PTFE (known 
also under the trade names Algoflon, Halon, Spectraion), must be calibrated in terms of the 
perfect reflecting diffuser (see CIE, 1979a; CIE, 1979b) for the required geometry. 



5. RECOMMENDATIONS CONCERNING GEOMETRIC CONDITIONS FOR 

COLORIMETRY 7 

Coiorimetric specifications are derived from spectral or tristimulus measurements. The 
measured values depend on the geometric relationships between the measuring instrument 
and the sample. These relationships are called "geometric conditions" or simply "geometry". 
Similarly, visual appraisals of coloured samples are affected by illuminating and viewing 
geometry. The degree of correlation between measured values and visual appraisals 
depends on the degree to which the geometric conditions of measurement simulate the 
geometric conditions of viewing. (The use of the term "viewing" with reference to measuring 



CIE 15:2004 



instruments is deprecated because it blurs the important distinction between instrumental 
measurements and visual observation.) 

Terms and definitions used in this Section of CIE 15:2004 introduce a terminology not 
used in previous versions of CIE 15, they are the following: 

reference plane 

plane in which the surface of a sample or standard is placed during measurements 
For reflection measurements, the geometry is defined with respect to the reference 
plane. For transmission measurements, there is a reference plane for the incident 
light and a second reference plane, displaced by the sample thickness, for the 
transmitted light. The recommendations of this publication are based on the 
assumption of negligible thickness. 

sampling aperture 

area of the reference plane on which measurements are made 
The sampling aperture is delimited by the area illuminated or by the area over which 
the receiver senses flux, whichever is smaller. If the illuminated area is the larger, the 
area measured is said to be "over filled"; if it is the smaller, the area measured is said 
to be "under filled". 

modulation 

generic term for measured ratios such as reflectance, reflectance factor or 
transmittance 

irradiation or influx (illumination or incidence) geometry 

angular distribution of irradiance at the centre of the sampling aperture 

reflection/transmission or efflux (collection, measuring) geometry 

angular distribution of receiver responsivity with respect to the centre of the sampling 
aperture 

Note: The influx and efflux geometry specify the geometric nature of the measurement. 

It is recommended that the geometry used when determining the colorimetric 
specification of diffusely reflecting samples corresponds to one of the following irradiating 
(influx) and reflection/transmission (efflux) conditions Vli . 

5.1 Recommended nomenclature for directional irradiation 

5.1.1 Forty-five degree directional geometry (45° x) 

Irradiation of reflecting materials at 45° to the normal, at one azimuth angle, emphasizes 
texture and directionality. The "x" in the symbol indicates that the azimuthal direction of the 
incident beam is in the x direction on the reference plane. 

5.1.2 Forty-five degree annular geometry (45° a) 

In measuring the colours of reflecting samples with 45° illumination, the effects of texture and 
directionality are minimized by irradiating at 45° to the normal, from all azimuthal directions, 
simultaneously. This irradiation (influx) geometry may be achieved by the use of a small 
source and an elliptic ring reflector or other aspheric optics. This geometry is sometimes 
approximated by the use of a number of light sources in a ring or a number of fibre bundles 
illuminated by a single source and terminated in a ring. Such an approximation to annular 
geometry is called circumferential geometry, symbol 45°c. 

5. 1.3 Zero degree directional geometry (0°) 
Irradiation of reflecting materials at the normal. 



VM Users of this report should check with the CiE list of publications for a technical report on 
this subject. 



CiE 15:2004 



5.1.4 Eight degree geometry (8°) 

Irradiation of reflecting materials at 8° to the normal, at one azimuth angle. It is used to 
substitute the zero-degree directional geometry in many practical applications, as in reflection 
measurements it permits differentiation between specular component included and excluded 
measurements. 

5.2 Recommended geometry for reflection measurements 

5.2. 1 Diffuse: eight-degree geometry, specular component included (di:8°) 

For di:8° geometry, it is recommended that the sample be irradiated by an integrating 
sphere 8 , that the measured area be overfilled, that the area of the sampling aperture be 
uniformly irradiated, that it be irradiated uniformly from all directions within the hemisphere 
bounded by its plane, that the responsivity of the receiver be uniform over the area of the 
sampling aperture, that the axis of the reflected (efflux) beam be 8° off the normal to the 
centre of the sample, and that radiation reflected at the sampling aperture be evaluated 
uniformly at all directions within 5° of the axis of the collection (efflux) beam. The size of the 
sampling aperture, area and angular uniformity of irradiation, angular displacement of the 
collected (efflux) beam from the normal, and area and angular uniformity of responsivity of the 
receiver can affect measured values and may be standardized in the future. 

5.2.2 Diffuse: eight-degree geometry, specular component excluded (de:8°) 

It is recommended that the specifications for di:8° be met, except that there be no radiation 
reflected in the direction of the receiver by a plane first-surface mirror at the sampling 
aperture and that there be no rays specularly reflected within 1° of such rays, as an allowance 
for instrumental scattering of stray light or misalignment. The amount of stray light specularly 
reflected in the direction of the receiver may affect measured values and may be 
standardized in the future. 

5.2.3 Eight degree: diffuse geometry, specular component included (8°:di) 

It is recommended that the conditions for di:8° be met, but with the light path reversed, so the 
sampling aperture is irradiated under 8° and flux reflected at the sampling aperture is 
collected at all angles in the hemisphere bounded by the reference plane. The sampling 
aperture should be underfilled with radiation. 

5.2.4 Eight degree: diffuse geometry, specular component excluded (8°:de) 

It is recommended that the geometric conditions for de:8° be met, but with the light path 
reversed. The sampling aperture should be underfilled with radiation. 

5.2.5 Diffuse / diffuse geometry (d:d) 

It is recommended that for irradiation the specifications for di:8° be met, and flux reflected at 
the sampling aperture is collected at all angles in the hemisphere bounded by the reference 
plane. In this geometry the sampling aperture can be neither underfilled nor overfilled. 

5. 2. 6 Alternative diffuse geometry (d:0°) 

An alternative diffuse geometry is the strict specular excluded geometry defined when the 
efflux direction is along the specimen normal. 

5.2. 7 Forty-five degree annular/ normal geometry (45°a:0°) 

It is recommended that the sampling aperture be irradiated uniformly from all directions 
between two right circular cones with their axes on the normal to the sampling aperture and 
apices at the centre of the sampling aperture, the smaller cone having a half angle of 40° and 
the larger of 50°. It is recommended that the receiver uniformly collects and evaluates all 
radiation reflected within a cone with its axis on the normal to the sampling aperture, apex at 
the centre of the sampling aperture, and a half angle of 5°. If this illuminating geometry is 
approximated by the use of a number of light sources in a ring or a number of fibre bundles 
illuminated by a single source and terminated in a ring, one gets the circumferential / normal 



CIE 15:2004 



geometry (45°c:0°). The above angular specifications should also hold for this geometry. 
These angular specifications and the surface and angular uniformity of irradiation and sensing 
may affect measured values and may be standardized in the future. 

5.2.8 Normal / forty-five degree annular geometry (0°:45°a) 

It is recommended that the angular and spatial conditions for 45°a:0° be met, with the light 
path reversed, so the sampling aperture is irradiated normally and reflected radiation is 
collected within an annulus centred at 45° to the normal. 

5. 2. 9 Forty-five degree directional / normal geometry (45°x:0°) 

It is recommended that the angular and spatial conditions for 45°a:0° be met with the 
exception that irradiation is only at one azimuth angle, this excludes the specular component, 
but emphasizes texture and directionality. The "x M in the symbol indicates that the azimuthal 
direction of the incident beam is in the x direction on the reference plane, 

5.2. 10 Normal / forty-Five degree directional geometry (0°:45°x) 

It is recommended that the angular and spatial conditions for 45°x:0° be met, with the light 
path reversed, so the sampling aperture is irradiated normally and reflected radiation is 
collected at one azimuth angle at 45° to the normal. 

Notes on recommended geometry for reflection measurements 

Note 1: Conditions 5.2.1, 5.2.2, 5.2.6, 5.2.7, 5.2.8, 5.2.9 and 5.2.10 give values of reflectance 
factor, R(A). For directional measurement with a sufficiently small angular spread, 
these values of reflectance factor become identical to values of radiance factor. For 
condition 5.2.3, for measuring with an ideal sphere, reflectance is measured. Thus, in 
the limit, the 45°x:0° condition gives the radiance factor f] 450 \ the 0°:45°x condition 
gives the radiance factor yft^; the di:8° condition gives the factor /? di:8 ; that 
approximates the radiance factor /? d . ; and the 8°:di condition gives the reflectance p 
(see CIE, 1987). 

Note 2: It is important that the particular irradiating and measuring conditions used should be 
specified even if they are within the range of one of these recommended standard 
conditions. Measurements of some types of samples (for example retro-reflective 
materials) may require different geometry or tolerances. 

Note 3: When integrating spheres are used, they should be fitted with white-coated baffles to 
prevent light passing directly between the sample and the spot of the sphere wall 
irradiated or measured. When the regular component of reflection is to be included, 
the sphere efficiency for that part of sphere wall that receives the regularly reflected 
radiation component should be of the same reflectance value as the sphere wall. The 
total area of the ports of the integrating sphere should not exceed 10 percent of the 
internal reflecting sphere area. 

Note 4: It should be noted that diffusing samples may scatter radiation in directions 
approximately parallel to their surfaces, and such radiation should be included in the 
measurement of diffuse reflectance. 

Note 5: When integrating spheres are used for measuring luminescent samples, the spectral 
power distribution of the irradiating system is altered by the reflected and emitted 
power from the sample (see CIE, 1988). The use of the 45°a:0°, 45°x:0° or 0°:45°a, 
0°:45°x condition is therefore preferable (see Gundlach and Mallwitz, 1976; Alman 
and BiSlmeyer, 1976). 

5.3 Recommended geometry for transmission measurements 

5.3.1 Normal / normal geometry (0°:0°) 

It is recommended that the irradiating (influx) and measuring (efflux) geometry be of identical 
right-circular conic form, with their axes on the normal to the centre of the sampling aperture, 
and half-angle of 5°, that the surface and angular irradiation of the sampling aperture be 



CIE 15:2004 



uniform, and that the surface and angular responsivity of the receiver be uniform. Deviation of 
axes from normal and variations in surface and angular conditions may affect measured 
values and may be standardized in the future. 

5.3.2 Diffuse / normal geometry, regular component included (di:0 °) 

It is recommended that the sampling aperture be uniformly irradiated from all directions in the 
hemisphere bounded by the first reference plane and that the measuring (efflux) beam be as 
specified for 0°:0° geometry. Deviation of the measuring (efflux) axis from normal and 
variations in surface and angular conditions may affect measured values and may be 
standardized in the future. 

5. 3. 3 Diffuse / normal geometry, regular component excluded (de:0°) 

It is recommended that the geometry be that specified for di:0° except that, with the sampling 
aperture open (i.e. no sample in place), there be no rays directed toward the receiver and no 
rays within 1° of such rays, as measured at the centre of the sampling aperture. 

5.3.4 Normal / diffuse geometry, regular component included (0°:di) 

It is recommended that the geometry be the reverse of that specified for di:0° geometry. 

5.3.5 Normal / diffuse geometry, regular component excluded (0 °:de) 

It is recommended that the geometry be the reverse of that specified for de:0° geometry. 

5. 3. 6 Diffuse / diffuse geometry (d:d) 

It is recommended that the sampling aperture be uniformly irradiated at all angles within the 
hemisphere bounded by the first reference plane and that the transmitted flux be uniformly 
evaluated at ail directions within the hemisphere bounded by the second reference plane. 

Notes on recommended geometry for transmission measurements 

Note 1: All the above conditions measure transmittance except for those where the regular 
component is excluded when the quantity measured is transmittance factor. 

Note 2: It is important that the particular irradiating and collecting conditions used are specified, 
even if they are within the range of one of the conditions recommended here. 
Measurements of some types of samples may require different geometry or tolerances. 

Note 3: Integrating spheres shall be fitted with white-coated baffles to prevent radiation 
passing directly from source to sample or reference in the case of diffuse irradiation 
or directly from sample or reference to detector in the case of diffuse collection. The 
total area of the ports of the integrating sphere should not exceed 10 percent of the 
internal reflecting sphere area. 

Note 4: The construction of an instrument for normal/normal measurements shall be such that 
the irradiating (influx) and collecting (efflux) beams shall be equal whether there is a 
sample in place or not. 

Note 5: It should be noted that diffusing samples may scatter radiation in directions 
approximately parallel to their surfaces, and such radiation should be included in the 
measurement of diffuse transmittance. 

Note 6: Multiple reflections between the sample and the incident beam optics if the incident 
beam is normal to the sample surface may cause measurement errors. These can be 
eliminated by slightly tilting the sample. 

6. RECOMMENDATIONS CONCERNING STANDARD OBSERVER DATA 9 

6.1 CIE 1931 standard colorimetric observer 

For correlation with visual colour matching of fields subtending between about 1° and about 
4° at the eye of the observer, it is recommended that colorimetric specifications of colour 



CIE 15:2004 



stimuli be based on the colour-matching functions x(A), y{X\ z(/l) 10 . A 2° visual field 

represents a diameter of about 17 mm at a viewing distance of 0,5 m. These colour-matching 
functions are given in the standard as values from 360 nm to 830 nm at 1 nm intervals with 
seven significant figures, and they define the CIE 1931 standard colorimetric observer (in 
technical applications often written as 2°-standard colorimetric observer) vll! . In the case where 
more coarsely sampled data will produce no significant calculation error, the tables 
reproduced in Section 1 1 may be used instead of the 1 nm interval data. The values given in 
Table T.4 at 5 nm intervals are selected values from the standard, rounded to six decimal 
places 11 . 

Note 1: x(A), y(A), z(X) are the normalized tristimulus values of monochromatic radiations for 
a set of reference stimuli [X], [Y], [Z] required to match each wavelength of the equi- 
energy spectrum. Their levels are such that the maximum of y(A)is unity and Ex(A) 

= lz(X) = Sy(2). (The equi-energy spectrum is radiation whose spectral 
concentration of power as a function of wavelength is constant.) 

Note 2: The real reference stimuli [R], [G], [B] of the original trichromatic system lead, by 
transformation, to [X], [Y], [Z]. y(X) is equated to V{X), the spectral luminous efficiency 

function for photopic vision, defining the CiE standard photometric observer for 
photopic vision (for more details see Appendix B). 

Note 3: The reference stimuli [X], [Y], [Z] were chosen for reasons of convenience in 
colorimetric computations. The colour-matching functions x(X) , y(X), z(X) are 
commonly used to obtain the tristimulus values X, Y, Z of colour stimuli (see Section 
7.1 for details). 

Note 4: If the colour-matching functions at closer intervals than given in Table T.4 are required, 
the values given in the CIE Standard S002 (CiE, 1986a) should be used. For 
interpolation at wavelength intervals smaller than 1 nm a linear interpolation should be 
used. 

Note 5: The chromaticity coordinates (see Section 7.3) x{X), y{A), z(X) of the spectral stimuli 
are the ratios 

x(A) + y(X) + I(X) 

y (X) = ^ 1^ _ (6.1) 

x(A) + y(X) + z(X) 



x(X) + y(X) + z(X) 

x(X) and y(X) are given in Table T.4. 

Note 6: The chromaticity coordinates x E , y E , z E of the equi-energy spectrum derived from the 
sums Zx(A), Sy(A),Sz(l) of Table T.4 are 

x E = 0,333 334 

y E = 0,333 331 (6.2) 

z E = 0,333 335 

The small differences between the values of the chromaticity coordinates x E , y E , z E 
are due to the limited number of decimal digits given in the table. 

6.2 CIE 1964 standard colorimetric observer 

For correlation with visual colour matching of fields of angular subtense greater than 4° at the 
eye of the observer, it is recommended that colorimetric specifications of colour stimuli be 



vm Table 1 of CIE standard colorimetric observers (CIE, 1986a) is reproduced in the CD-ROM 
that accompanies this Technical Report. 



10 



CiE 15:2004 



based on the colour-matching functions x 10 (A) ) yio(^). z io(^) published in the CIE Standard: 
CIE standard coSorimetric observers (CIE, 1986a). A 10° visual field represents a diameter of 
about 90 mm at a viewing distance of 0,5 m. These colour-matching functions are given in the 
standard as values from 360 nm to 830 nm at 1 nm intervals with six significant figures, and 
they define the CIE 1964 standard colorimetric observer (in technical applications often 
written as 10°-standard colorimetric observer) lx in the case more coarsely sampled data will 
produce no significant calculation error, the tables reproduced in Section 1 1 may be used 
instead of the 1-nm interval data. The values given in Table T.5 at 5 nm intervals are selected 
values from the standard, rounded to six decimal places. 

Note 1: x 10 (A),y 10 (A),z 10 (>l) are the normalized tristimulus values of monochromatic 

radiations for a set of reference stimuli [X 10 ], [Y 10 ], [Z 10 ] required to match each 
wavelength of the equi-energy spectrum. Their levels are such that the maximum of 
y w (A) is unity and 2x 10 (A) = 2y 10 U) = £z 10 (>l) (The equi-energy spectrum is 
radiation whose spectral concentration of power as a function of wavelength is 
constant.) 

Note 2: The real reference stimuli [R 10 ], [G 10 ], [B 10 ] of the original trichromatic system are 
related by transformation to the reference stimuli [X 10 ], [Y 10 ], [Z 10 ], which were 
chosen for reasons of convenience in colorimetric computations (see Appendix B). 
The colour-matching functions, x 10 (2), y 10 (A), z 10 (/t) are commonly used to obtain the 
tristimulus values X 10 , Yio, Z 10 of colour stimuli. 

Note 3: If the colour-matching functions of Table T.5 are required at closer intervals, the values 
at 1 nm intervals given in the standard, CIE standard colorimetric observers (CIE, 
1 986a) should be used. For values at other than the 1 nm intervals see Note 4 to 6. 1 . 

Note 4: The chromaticity coordinates x 10 (A), y 10 (A), z 10 (^) of the spectral stimuli are the ratios 

x 10 (A) = ^ ! 1o(A) _ 

x 10 (;i)+y 10 (/i) + z 10 (;,) 

y 10 W=- I"™ _ (6.3) 

XioW+yioW + ^oW 



ZioW = 



*io(>0 



xioW+yioW+zioW 

x 10 (A) and y 10 (A) are given in Table T.5. 

Note 5: The chromaticity coordinates x 10 , E , yio,E» *io,e of the equi-energy spectrum derived 
from the sums Ix 10 (2), Sy 10 (/L), Ez 10 (A) of Table T.5 are 

X| 0> e = 0,333 298 

y,o, E = 0,333 336 (6.4) 

Zio.e = 0,333 366 

The small differences between the values of the chromaticity coordinates x 10E , y 10 E, 
z 10E are due to the limited number of decimal digits given in the table. 

Note 6. The large-field colour matching data as defined by the CIE 1964 standard colorimetric 
observer are intended to apply to matches where the luminance and the relative 
spectral power distributions of the matched stimuli are such that no participation of 
the rod receptors of the visual mechanism is to be expected. This condition of 
observation is important as "rod intrusion" may upset the predictions of the standard 
observer. For daylight, possible participation of rod vision in colour matches is likely 
to diminish progressively above about 10 cd-rrf 2 and be entirely absent at about 
200 cd-m" 2 . For further details see 12 . 



iX Table 2 of CiE standard colorimetric observers (CIE, 1986a) is reproduced on the CD-ROM 
that accompanies this Technical Report. 



11 



X = kZfa{A)xW)AA 


X w = k w £^(A)x w (A)AA 

A 


Y = kj^(A)y(A)AA 


Vio=*iof*iW)7ioW^ 


Z = kZ<j> k {X)z{A)AA 


Z 10 =^ 10 2-^(A)z 10 (/t)zl/l 

A 



CIE 15:2004 



The CIE 1931 and 1964 standard colorimetric observers were both derived from 
trichromatic systems based on real red [Rj, green [G] and blue [B] primaries, see Appendix B. 



7. RECOMMENDATIONS CONCERNING THE CALCULATION OF TRiSTIMULUS 

VALUES AND CHROMATICITY COORDINATES 13 

7.1 Calculation of tristimulus values 

The CIE Standard (CIE, 1986a) on standard colorimetric observers recommends that the CIE 
tristimulus values of a colour stimulus be obtained by multiplying at each wavelength the 
value of the colour stimulus function <p x {A) by that of each of the CIE colour-matching 
functions and integrating each set of products over the wavelength range corresponding to 
the entire visible spectrum, 360 nm to 830 nm. The integration can be carried out by 
numerical summation at wavelength intervals, AA, equal to 1 nm. 



(7.1) 



In the above equations <fi ? {A) denotes the spectral distribution of the colour stimulus 
function, i.e. fa(A) = d^ytU, see CIE international Lighting Vocabulary item 845-01-17 (CIE, 
1987). X, Y,Z are tristimulus values, x(A),y(A),z(A) are colour-matching functions of a 
standard colorimetric observer, and k is a normalising constant defined below. Each of these 
may be specified for the CIE 1931 standard colorimetric system by being written without a 
subscript, or for the CIE 1964 standard colorimetric system by the use of the subscript 10. 

The fundamental colorimetric tables are the 1 nm tables in CIE standards. All 
rigorous calculations should use these 1 nm tables. For most practical purposes, the 
summation may be approximated by using wavelength intervals, AX equal to 5 nm over the 
wavelength range 380 nm to 780 nm. Values of the CIE colour-matching functions at 5 nm 
intervals suitable for use in summation over this range of wavelengths are given in Tables T.4 
and T.5. When measurements have been made at smaller intervals than 5 nm, the 
appropriate values from the tables in the standards should be used. 

Tristimulus values are usually evaluated on a relative basis. In such cases the 
relative colour stimulus function, tp (A), may be used instead of the colour stimulus function, 
fa{A) y but it is essential that, for stimuli that will be considered together, all the spectral 
distributions involved be assessed on the same relative basis. The tristimulus values obtained 
are then relative in the sense that all the values involved may be multiplied by the same single 
arbitrary constant. In certain cases, however, k and /c 10 must be chosen according to agreed 
conventions; these are explained in Sections 7.1.1 and 7.1.2. 

Tristimulus values evaluated on a relative basis may need to be supplemented by the 
value of a suitable absolute photometric quantity. 

7.1.1 Secondary light sources (reflecting or transmitting objects) 

For reflecting or transmitting object colours, the colour stimulus function, ^(A), is replaced by 
the relative colour stimulus function, <j> {A), evaluated as 

(HA) = R(A)-S{A) or <&A) = r{A)-S{A) 

where; R(A) is the spectral reflectance factor (or spectral radiance factor or spectral 
reflectance) of the object colour (preferably evaluated for one of the geometric 
conditions given in Section 5.2). 

t{A) is the spectral transmittance of the object colour (preferably evaluated for one 
of the geometric conditions given in Section 5.3). 

S(A) is the relative spectral power distribution of the illuminant (which, whenever 
12 



CI E 15:2004 

possible, should be one of the CIE standard illuminants; see Section 3.1). 
In this case, the constants, k and /c 10 , are chosen so that Y = 100 for objects for which 
R(£), or r{A) = 1 for all wavelengths, and hence 

k = 10Q/J^S{A)y(A)AA 

(7.2) 
* 10 =100/£S(A)y 10 U)A>l 

A. 

For other objects, the values of Y are then equal to the percentage values of 
iuminous reflectance factor or luminance factor or luminous reflectance [in the case of R{A)], 
or luminous transmittance or luminous transmittance factor [in the case of t(A)]\ this is 
because the y(A) function is identical to the CIE spectral luminous efficiency function V(A)\ 

7.1.2 Illuminants and self-luminous objects 

For self-luminous objects and illuminants, the constants, k and /c 10 , are usually chosen on the 
grounds of convenience. If, however, in the CIE 1931 standard colorimetric system, the Y 
value is required to be numerically equal to the absolute value of a photometric quantity, the 
constant, k, must be put equal to the numerical value of K m , the maximum spectral luminous 
efficacy (which is equal to 683 Im-W 1 ) and fa{A) must be the spectral concentration of the 
radiometric quantity corresponding to the photometric quantity required. 

7.2 The use of abridged or truncated data 

The use of the tables published in the CiE standard on colorimetric observers (CIE, 1986a) 
requires that the colour stimulus function, $ z (a), or the relative colour stimulus function, #(Z), 
be known at 1 nm wavelength intervals over the wavelength range 360 nm to 830 nm. In 
practical applications, all the required data may not be available because the measurement 
was made at intervals greater than 1 nm, or unequal wavelength intervals were used, or data 
at the spectral extremes were omitted (truncation). Often it is possible to predict the needed 
but unmeasured data. It is recognised that calculation from predicted, rather than from 
measured, data, or from abridged or truncated data, may be inexact, but the investigator can 
often be satisfied that the accuracy is sufficient for the intended use of the tristimulus values. 
It is important to use the same wavelength interval and range throughout for any set of 
calculations in which data for different colours are to be compared precisely. In particular, it 
should be noted that the exact values obtained for the perfect diffuser for a given illuminant 
depend on the wavelength interval and range used 14 . 

7.2.7 Abridgement 

Abridgement of colour stimulus data by the use of a larger sampling interval, for example 
10 nm or 20 nm, wiil lead to errors in the computed tristimulus values. Such abridgement 
should be used only when it can be demonstrated that these errors are negligibly small for the 
intended use of the tristimulus values. If these errors are not negligible, it is recommended 
that needed but unmeasured values of <fi z (A) } R(A), or zfA) be predicted by adequate 
interpolation. 

Note 1: Spectral reflectance and transmittance curves are usually smooth enough and 
continuous to permit interpolation, while e.g. spectral power distribution data of gas 
discharge lamps are frequently not suited for interpolation. Using interpolated values 
of spectral power distribution data of such lamps may lead to considerable errors. 



x CIE Division 1 is currently investigating whether a V^ Q (A) function should be introduced, 
where V W (A) ~ y 10 (A). interested parties should check the latest CIE publication list or the 
recent edition of the International Lighting Vocabulary on the introduction of such a new 
definition. At the closing of the present edition of CIE 15 no V^ q {a) function has been officially 
agreed (for further details see Appendix B). 



13 



CIE 15:2004 



Note 2: Measurement errors also arise from the bandwidth of a spectrometer. Even if the data 
interval is 1 nm, the colorimetric errors can be significant if the bandwidth of the 
spectrometer is large. See 7.2.5 for bandwidth requirements. 

7.2.1.1 Interpolation 

Use one of the four following methods to calculate needed but unmeasured values of fa(A), 
R{a) or r(X) within the range of measurements: 1) the third-order polynomial interpolation 
(Lagrange) from the four neighbouring data points around the point to be interpolated, or 2) 
cubic spline interpolation formula, or 3) a fifth order polynomial interpolation formula from the 
six neighboring data points around the point to be interpolated, or 4) a Sprague interpolation 
(see Seve, 2003) XI 

Note: Experiments have shown that for most samples showing smooth reflectance or 
transmittance spectra, the computed tristimuius values will have an adequate 
accuracy if measured data, illuminant and colour-matching function values at 5 nm 
intervals are used. See also Note to Section 7.2.3. 

7.2.2 Truncation 

Where the measurement range is less than the practical range of summation, 380 nm to 
780 nm, omission of values at the limits of the measurement range will lead to errors in the 
computed tristimuius values. Such truncation should be used only when it can be demonstrated 
that these errors are negligibly small for the intended use of the tristimuius values. 

Note; If these errors due to limited measurement range are not negligibly small, the errors 
might be reduced by adequate extrapolation of the needed but unmeasured values of 
<j>iX), R(Z) or t(A). The range of the summation is an essentia! part of the tristimuius 
specification. 

7.2.2.1 Extrapolation 

Extrapolation is generally not recommended. However, when predicting needed but 
unmeasured values of ^(A) or <f{X) outside the range of measurements, in the absence of 
other information, unmeasured values of fa(Z), [$(%)] or of p(A), /?(A), or r(X) may, as a rough 
approximation, be set equal to the nearest measured value of the appropriate quantity in 
truncation. 

7.2.3 Weighting factors 

In the case of repetitive calculations from measurements at the same wavelengths, it is often 
convenient to perform only once those calculations that are independent of the measured 
data. This results in a table of weighting factors. Such weighting factors should give results 
consistent with those from the normal calculations. It is recommended that tables of weighting 
factors be calculated for the full range of wavelengths, 360 nm to 830 nm. This provides 
tables that may be used for any degree of truncation by adding the weights at the 
unmeasured wavelengths to those at the extreme measured wavelengths. The sum of the 
weights at the unmeasured wavelengths is a measure of the maximum error introduced by 
truncation. 

Note: If it has been checked that measurement data obtained only at 10 nm or 20 nm 
intervals satisfy the need of the observer, computation methods as described e.g. in 
ASTM (1999) might be used. This publication contains weighting factors for both the 
CIE 1931 standard colorimetric observer and the CIE 1964 standard colorimetric 
observer and a number of illuminants and practical light sources used in colorimetry. 
Its Table 5 has been developed for the case when the instrument manufacturer has 
built in a correction to zero bandwidth (see Fairman, 1985). Its Table 6 provides 



XI 



A CIE Technical Committee is currently working on a standardized method of interpolation, 
interested parties should check the latest CIE publication list for more information. The CD- 
ROM accompanying this report contains PC interpolation programs for linear, Lagrange, 
spline and Sprague interpolation. 



14 



CIE 15:2004 



weighting factors for the case when a correction to a zero bandwidth is required (see 
also Venable, 1989; Li et al., 2004; ASTM, 2001 and ASTM, 2003). 

7. 2. 4 Numerical procedures 

It is recommended that all numerical calculations be carried out using the full number of 
significant digits provided by the data in the Tables published in the CIE standards of 
colorimetry. Final results should be rounded to the number of significant digits indicated by 
the precision of the measurements. 

Note 1 : For the purpose of calculating tristimulus values, the quantities involved for secondary 
light sources shall be defined as points of a continuous distribution, each point 
representing an infinitely narrow range of wavelengths. For primary light sources the 
relative emitted power is regarded as emitted in a wavelength band equal to the 
measuring interval and centred around the nominal wavelength. 

Note 2: For colour stimulus functions of primary light sources that vary rapidly with 
wavelength, the spectral bandwidth at half power of the measuring instrument used to 
determine the colour stimulus function should be equal to, or an integer multiple of, 
the measuring interval. For smoothly varying functions this restriction is less 
important. For the highest accuracy, a bandwidth of 1 nm may be used for the 
measuring instrument, but for most practical purposes a bandwidth and measurement 
interval of 5nm may be used. The use of bandwidths of 10 nm, or 20 nm is not 
recommended; it can lead to considerable loss of accuracy, and if applied, should be 
checked on typical spectra. For practical measurements a trade-off between 
bandwidth and signal-to-noise ratio has to be found, as the latter will influence 
photometric accuracy. A signal-to-noise ratio of 1 : 1 0" 4 when measuring an ideal white 
sample is adequate for most applications. 

Note 3: The foregoing recommendations are based on measurements at equal intervals of 
wavelength, it is, however, not intended to imply that summations may properly be 
computed only with such intervals. Other summation procedures, including 
specifically the method of selected ordinates, may be used providing that the 
tristimulus values thus computed are consistent with those based on the above 
recommendations. 

7. 2. 5 Bandwidth of a spectrometer 

When discussing errors associated with data intervals, it is also important to know 
measurement errors (uncertainties) due to the bandwidth of a spectrometer because, in real 
measurements, the data interval (scanning interval) and the bandwidth are closely related 
with each other to affect the measurement results. 

Measurement errors arising from the bandwidth of a spectrometer are generally much 
larger (by an order of magnitude) than the calculation errors associated with data intervals. 
Even if the data interval is 1 nm (or interpolated to 1 nm intervals), the colorimetric errors can 
be significant if bandwidth of the spectrometer is large. See also Section 7.2.4 Note 2. 

7.3 Calculation of chromaticity coordinates 

It is recommended that chromaticity coordinates (x, y, z) be derived from the tristimulus 
values (X, Y, Z) as follows; 

X 



X + Y + Z 



y -x^kz (73) 

z 

z =- 



X + Y + Z 



Because of the relation x + y+z=1,it suffices to quote x, y only. The diagram using 
the chromaticity coordinates x, y is referred to as the CIE 1931 chromaticity diagram or the 
CIE (x, y) (chromaticity) diagram. 



15 



CIE 15:2004 



Note: The chromaticity coordinates x 10 , yio, z w are computed simiiarly from the tristimulus 
values X 10 , V10 , Z 10 ; the CIE 1964 chromaticity diagram is obtained using these 
values. 

7.4 Equations representing relationships between colour stimuli 16 

When equations are used to represent relationships between colour stimuli, symbols of vector 
notation should be used instead of those for numerical relationships. For example, one of the 
following forms could be used: 

[C].X[X]+Y[Y] + Z[Z] 

or (7.4) 

C = XX+YY+ZZ 

where X } Y } Z are the tristimulus values of colour stimulus [C], or C. The unit vectors of the 
reference stimuli are indicated either by [X], [Y], [Z], or by the boldface Roman letters X, Y, Z. 
Note: In Equ. 7.4 the "= ' and "=" signs mean "matches". 



8. RECOMMENDATIONS CONCERNING UNIFORM COLOUR SPACING AND 

COLOUR DIFFERENCES 16 

8.1 CIE 1976 uniform chromaticity scale diagram (UCS diagram) 

The use of the following chromaticity diagram is recommended whenever a projective 
transformation of the (x.yj-diagram yielding colour spacing perceptually more uniform than 
that of the (x,y)-diagram is desired. The chromaticity diagram is produced by plotting 

u' = 4X/(X+15Y+3Z) 
as abscissa and (8.1) 

v 1 =9YI(X+ 15Y+3Z) 

as ordinate, in which X, V, 1 are tristimulus values. The third chromaticity coordinate w' is 
equal to (1 - u' - v 1 ). 

Note 1: The colour spacing afforded by this chromaticity diagram is known to be perceptually 
more uniform than that of the CIE (x f y)-chromaticity diagram for observation of 
samples having negligibly different luminances (e.g. for AY<0,5). This diagram is 
intended to apply to comparisons of differences between object colours of the same 
size and shape, viewed in identical white to middle-grey surroundings, by an observer 
photopically adapted to a field of chromaticity not too different from that of average 
daylight. 

Note 2: The same chromaticity diagram is produced by plotting 

u'= 4x / (-2x + 1 2y + 3) as abscissa and 

v' = 9y / (-2x + 1 2y + 3) as ordinate, (82) 

where x, y are chromaticity coordinates. 

Note 3: If the angle subtended at the eye by the pairs of specimens being compared is more 
than 1° and less than about 4°, the tristimulus values X, Y, Z (or chromaticity 
coordinates x, y), calculated using the CIE 1931 standard colorimetric observer 
should be used for the calculation of u' and v'. If the angle is greater than 4°, the 
tristimulus values X 10 , Y 10 , Z 10 , (or chromaticity coordinates x 10 , yio) of the CIE 1964 
standard colorimetric observer should be used to calculate u\ and v' 10 . 

Note 4: The CIE 1960 UCS diagram, now obsolete, is described briefly in Appendix A.3. 

8.2 CIE 1976 uniform colour spaces 

Pending the development of an improved coordinate system 17 , the use of one of the following 
coordinate systems is recommended whenever a three-dimensional spacing perceptually 
more nearly uniform than that provided by the XYZ system is desired. 



16 



CIE 15:2004 



8.2.1 CIE 1976 (L*a*b*) colour space; CIELAB colour space 

8.2.1.1 Basic coordinates 

Three-dimensional, approximately uniform, colour space produced by plotting in rectangular 
coordinates, L* a* b*> quantities defined by the equations 



Z_* = 116f(WY n )-16 






(8-3) 


a* = soo[/(x/Xn)-/(y/y„)] 






(8.4) 


b* = 2QQ[f{YIY n )-f{ZIZ n )] 






(8.5) 


f(X/X n ) = (X/X n ) 1/3 


if 


(X/X n )>(24/116) 3 


(8.6) 


f(X/X n ) = (841/108)(X/X n )+16/116 


if 


(X/X n )<(24/116) 3 


(8.7) 


f(y/y n )-(wy n ) 1/3 


if 


(y/y n )> (24/1 16) 3 


(8.8) 


f{Y/Y n ) = (841/108)(Y/y n ) +16/116 


if 


(y/y n )< (24/1 16) 3 


(8.9) 


f(Z/Z n ) = (Z/Z n ) 1/3 


if 


(Z/Z n )> (24/1 16) 3 


(8.10) 


/(Z/Z n ) = (841/108)(Z7Z n ) +16/116 


if 


(Z/Z n )< (24/1 16) 3 


(8.11) 



where 



and 



and 



where X,Y,Z are the tristimulus values of the test object colour stimulus considered and X n , 
y n; Z n are the tristimulus values of a specified white object colour stimulus. In most cases, the 
specified white object colour stimulus should be light reflected from a perfect reflecting 
diffuser illuminated by the same light source as the test object. In this case, X n , Y n , Z n are the 
tristimulus values of the light source with Y n equal to 100 18 \ 

The informative annex Appendix D describes the recommended reverse 
transformation of the L*, a*, b* coordinates to X, Y, Z tristimulus values. 

8.2.1.2 Correlates of lightness, chroma and hue 

Approximate correlates of the perceived attributes lightness, chroma and hue are calculated 
as follows 

CIE 1976 lightness: L* as defined in Equ. 8.3. 

CIE 1976 a,b (CIELAB) chroma : C* ab = (a* 2 + 5* 2 ) 1/2 (8.12) 

CIE 1976 a ; b (CIELAB) hue angle: h ab = arctan (bVa*) (8.13) 

see Section 8.2.3 Note 1 and Note 2. 

8.2.1.3 Colour differences 

Euclidean distances in CIELAB colour space can be used to represent approximately the 
perceived magnitude of colour differences between object colour stimuli of the same size and 
shape, viewed in identical white to middle-grey surroundings, by an observer photopically 
adapted to a field of chromaticity not too different from that of average daylight. In cases of 
deviating conditions the correlation between calculated and perceived colour differences may 
be impaired. 

Differences between two samples (denoted by subscripts and 1) shall be calculated 
as follows: 

CIELAB lightness difference: A/_* = L\ - L\ (8.14) 

Aa* = a* 1 -a* (8.15) 

Ab* = b\ - b* (8.16) 

CIELAB chroma difference: AC* ab = C* ab ,i - c Vo (8.17) 



17 



CIE 15:2004 



CIELAB hue angle difference: A/? ab = h abtl - h abi p (8.18) 

If the line joining the two colours crosses the positive a* axis, Equ. 8.18 will give a value 
outside the range ±180°, in this case, the value of Ah ab must be corrected by adding or 
subtracting 360° to bring it within this range, see also Section 8.2.3 Note 4. 

CIELAB hue difference AH* ab = 2(C* abir C* abj0 ) 1/2 -sin(A/? ata /2) (8.19) 

for small colour differences away from the achromatic axis 

AH% b = (C* ab( rCVo) 1/2 -A^ ab (8.20) 

where the value of A/? ab is in radians. 

Note 1: The calculation of CIELAB hue and chroma differences is progressively less useful as 
the absolute value of Ah ab approaches 1 80°. 

Note 2: In information technology and other fields the subscript (R) is sometimes used for 
reference and (T) for test instead of (0) and (1). Similarly in industrial evaluation of 
small colour differences (s) is sometimes used for standard and (b) for batch. 

CIE 1976 a,b (CIELAB) colour difference, AE* ab between two colour stimuli is calculated as 
the Euclidean distance between the points representing them in the space: 



AE* ab =lAL*Y+{Aa*Y+(*b*f]' 2 



(8.21) 



or 



AE 



ab 



M" 



+ |AC* ab | +\AH" 



(8.22) 



these two definitions of AE* ab are equivalent. 

Alternative ways of calculating AH* ab are: 



AH 



ab ■ 



(AE*J-(M*y-(*C*Jj 



where AE* ab is calculated from Equ. 8.21 , and AH* ab has the same sign as A/? ab ; 

-|1/2 

AH% b =/f2JCVi-C* ab ,o-aVa*o-bVfcV 



(8.23) 



(8.24) 



where k = -1 if a *, • b * > a * • b * 1 , otherwise k = 1 ; 



and 



AH* ab = \a\-b%-a\-b\ I 



0,5C* aby C% bfl+ a%-a\+b%-b* 



1/2 



(8.25) 



More details on these alternative methods of calculating A/-/* ab are given in Seve 
(1991), Stokes and Brill (1992) and Seve (1996). 

Note: In different practical applications it may be necessary to use different weightings for 
AL*, AC* ab) and A/-/* ab . In 2001, the CIE recommended such weightings in a new 
formula for industrial evaluation of small colour differences (CIE, 2001a), see Section 
8.3. 



8.2.2 CIE 1976 (L*u*v*) colour space; CIELUV colour space 

Three-dimensional, approximately uniform, colour space produced by plotting in rectangular 
coordinates, L* u*, v*, quantities defined by the equations 

L* = 116 f(YIY n )- 16 
See also Equ. 8.3, where 



nyiYn) = (YiY n ) 



if (WV n ) > 



24 
TT6 



(8.26) 
(8.27) 



18 



CI E 15:2004 



f(Y/Y n ) = (841/108)(Y/Y n ) +16/116 if (V/V n ) < I — 1 (8.28) 

J16J 



and 



u* = 13L*(u'-u'n) (8.29) 

v* = 13L*(v' - v' n ) (8.30) 

where Y, u', v' describe the colour stimulus considered and Y n , u' n , v' n describe a specified 
white object colour stimulus. 

Approximate correlates of lightness, saturation, chroma, and hue may be calculated 
as follows: 

CIE 1976 lightness: L* as defined in Section 8.2.1.1 

and Equ. 8.26. 
CIE 1976 u } v (CIELUV) saturation: s u , v = 1 3 [(u' - u' n ) 2 + {vW n f] m (8.31) 

CIE 1976 u,v (C1ELUV) chroma: C* uv = (u* 2 + v* 2 ) 1 ' 2 = L*s w (8.32) 

CIE 1976, u.y (CIELUV) hue-angle: h m = arctan[(v' - v' n )!(u' - u\)\ 

= arctan(v*/u*) (8.33) 

See 8.2.3, Note 2. 

CIE 1976 u, v (CIELUV) hue-difference: AH* UV = 2(C Vi • C * uv ,o) 1/2 sin(A/) uv /2) (8.34) 

where 1 and refer to the two samples between which the colour difference is to be 
calculated and A/7 UV = h uvA - /? UVi0 (see Seve ,1991). 

CIELUV colour difference A£* uv between two colour stimuli is calculated as the Euclidean 
distance between the points representing them in the space: 

AE* UV = [(AL*) 2 + (Au*f + (Av*) 2 ] 1/2 (8.35) 

For an alternative ways to calculate AH* UV , see the description in 8.2.1 , but change a* 
to u* and b* to v*. 

8.2.3 Notes on CIE 1976 uniform colour spaces 

Note 1: When the linear formulae (Equ.'s 8.7, 8.9 or 8.11) are used for X/X n , Y/Y n ox ZIZ n , 
anomalous values of h ab may be obtained (McLaren, 1980). Anomalous values are 
unlikely to occur for surface colours but may occur for transparent object colours of 
low luminance factor lying close to the spectrum locus or purple line. 

Note 2: h ab (or h uv ) lies between 0° and 90° if a* and b* (or u* and v*) are both positive, 
between 90° and 180° if b* (v*) is positive and a* (u*) is negative, between 180° and 
270° if b* and a* (v* and u*) are both negative, and between 270° and 360° if b* (v*) 
is negative and a* (u*) is positive. 

Note 3: CIE 1976 a,b and u,v hue-differences are introduced so that a colour difference AE* 
can be broken up into components AL*, AC* : and AH* whose squares sum to the 
square of AE*. Differences in CIE 1976 a,b or u,v hue-angle, &h ab (or A/? uv ), do not 
have this property. 

Note 4: If the line joining the two colours crosses the positive a* (or u*) axis, the value of A/7 ab 
(or Ah uv ) must be corrected by adding or subtracting 360° to bring it into the range 
±180°. 

Note 5: These spaces are intended to apply to comparisons of differences between object 
colours of the same size and shape, viewed in identical white to middle-grey 
surroundings, by an observer photopically adapted to a field of chromaticity not too 
different from that of average daylight. 

Note 6: If the angle subtended at the eye by the pairs of object colours being compared is 
between about 1° and 4° the tristimulus values X, Y, Z calculated with respect to the 
CIE 1931 standard colorimetric observer should be used for the calculation of L* a* 
/>*, u* v* and hence AE* ab , C* ab , s uv , C* uv , h ab , h uv , AH* ab , AH* UV . If the angle is greater 



19 



CIE 15:2004 



than 4°, the tristimulus values X 10 , V 10l Z 10 calculated with respect to the CIE 1964 
standard colorimetric observer should be used to calculate L* 10 , a* 10 , *>*io. u* 10 , v*io, 
and hence AE* a b,ioi C* a b,ioi s uv,ioj C* UVi io. ^at>,io, ^Wioi ^^*ab,io. AH* UVj io- 

Note 7: The obsolete CIE 1964 uniform colour space and colour difference formula are 
described briefly in the Appendix A. 

Note 8: In different practical applications it may be necessary to use different weightings for 
AL*, AC*, and AH*, see Section 8.3. 

Note 9: Equ.'s 8.21 to 8.25 and 8.35 have been replaced for small colour differences by the 
new recommendation of the CIE, see Section 8.3. 

8.3 Improved industrial colour difference evaluation 



8.3. 1 CIEDE2000 total colour difference formula 

The CIE 1976 uniform colour spaces provide for the calculation of colour differences as 
vector distances in those spaces, industrial practice with small colour differences has shown 
non-uniform effects with calculated values in different ranges and different directions in those 
spaces. Moreover, a change of external observing conditions may change the perceived 
magnitude of the colour difference in a sample pair. The work documented in CiE 101-1993 
(CIE, 1993) describes a number of external parameters of a visual task that affect the 
correlation of visual magnitude judgements of colour differences with their colorimetric 
measures. The outcome of those studies was the definition of reference conditions of a visual 
task to which a colour-difference formula should be adapted. Experimental data sets must 
now be chosen to meet reference conditions or to clearly define quantified deviations from 
them. 

The CIEDE2000 total colour difference formula corrects for the non-uniformity of the 
CIELAB colour space for small colour differences under reference conditions. Improvements 
to the calculation of total colour difference for industrial colour difference evaluation are made 
through corrections for the effects of lightness dependence, chroma dependence, hue 
dependence and hue-chroma interaction on perceived colour difference. The scaling along 
the a* axis is modified to correct for a non-uniformity observed with grey colours. The 
resulting recommendation is as follows (CIE, 2001a) Xh : 



^00 = 



AL' 
k L S L 



AC 



AH' 



+ R T 



( AC 



AH' 



& 



(8.36) 



A localized modification of the scaling along the a* (red-green opponent) axis is made 
to improve agreement with visual colour-difference perception for neutral colours. The 
modification increases the magnitudes of a' values compared to a* values for colours at low 
chroma. The transformation is as follows: 



L'=L* 

a'^a*{UG) 

b'=b* 



(8.37) 



G=0,5 



1 i 



*7 
ab 



c 



+25 7 



(8.38) 



The transformed L', a', b' values are used in calculation of hue angle, chroma and 
lightness, chroma and hue differences and these quantities are designated by a prime mark 
in the equations. 



Xil We follow here the terminology used in CIE 142-2001 (CIE, 2001a), and omit the subscript 
"10", although C1EDE2000 is recommended for sample size larger than 4 degrees and thus 



the 10 degree observer has to be used. 



20 



CIE 15:2004 

Weighting functions, S L , S c , S H adjust the total colour-difference for variation in 
perceived magnitude with variation in the location of the colour-difference pair in L' a', b' 
coordinates. 

Sl=1+ 0/015 (/?~50f (8.39) 

V20 + (l'-50]P 

S C =1 + 0,Q45C' (8.40) 

S H =1 + 0,015CT (8.41) 

T -1-0,17 cos(/?-3o) +0,24 cos(2h')+0,32 cos(3rt'+6)-0,20 cos(4/t"'-63) (8.42) 

Visual colour-difference perception data show an interaction between chroma 
difference and hue difference in the blue region that is observed as a tilt of the major axis of a 
colour-difference ellipsoid from the direction of constant hue angle. To account for this effect, 
a rotation function is applied to weighted hue and chroma differences. 

R r = -$\n(2AG)R c (8.43) 

A0 - 30exp {- [(/?-275)/25J 2 } (8.44) 



R C -2J^ 7 C ' 7 _ (8.45) 

Mean hue angle and A6> values are in degree units. 

Note 1 : All quantities with a super-position bar indicate the mean of the values for each of the 
samples of a colour-difference pair. 

Note 2: The parametric factors, k L , /c c , k H are correction terms for variation in experimental 
conditions. Under reference conditions they are all set at 1 . For other choices see 
(CIE, 1993). The reference conditions are: 

Illumination: source simulating the spectral relative irradiance of CIE 

standard iiluminant D65. 

Illuminance: 1000 Ix. 

Observer: normal colour vision. 

Background field: uniform, neutral grey with /_* = 50. 

Viewing mode: object. 

Sample size: greater than 4 degrees subtended visual angle. 

Sample separation: minimum sample separation achieved by placing the sample 

pair in direct edge contact. 
Sample colour- 
difference magnitude: to 5 CIELAB units. 

Sample structure: homogeneous colour without visually apparent pattern or non- 
uniformity. 

Note 3: An alternative colour difference formula (CMC formula) not developed by the CIE, but 
used by some ISO committees, is briefly described in Appendix A.5 for reference 
purposes. 

Note 4: A further colour difference formula based on a modified colour space derived from 
CIELAB is the DIN 99 formula (DIN, 2003), see Appendix A 6. 



21 



CIE 15:2004 



9 RECOMMENDATIONS CONCERNING MISCELLANEOUS COLORIMETRIC 

PRACTICES AND FORMULAE 

9.1 Dominant wavelength and purity 19 

When it is desired to express chromaticity in terms of dominant (or complementary) 
wavelength and purity, it is recommended that the evaluations be carried out as follows. 

9.1.1 Dominant wavelength (of a colour stimulus), A^ 

Wavelength of the monochromatic stimulus that, when additively mixed in suitable proportions 
with the specified achromatic stimulus, matches the colour stimulus considered. 

Note: For stimuli whose chromaticities lie between those of the specified achromatic 
stimulus and the two ends of the spectrum, complementary wavelength is used 
instead of dominant wavelength. 

9.1.2 Complementary wavelength (of a colour stimulus), ^ 

Wavelength of the monochromatic stimulus that, when additively mixed in suitable proportions 
with the colour stimulus considered, matches the specified achromatic stimulus. 

Note: See note to dominant wavelength. 

9.1.3 Colon metric purity, p c 
Quantity, p c , defined by the relation 

p c = L d /(L d + L n ) (9.1) 

where L d and L n are, respectively, the luminances of the monochromatic stimulus and of the 
specified achromatic stimulus that match the colour stimulus considered in an additive 
mixture. 

Note 1: In the case of stimuli characterized by complementary wavelength, suitable mixtures 
of light from the two ends of the spectrum are used instead of the monochromatic 
stimulus, and colorimetric purity should then be calculated using the equation given in 
Note 2. 

Note 2; in the CiE 1931 standard colorimetric system, colorimetric purity is related to 
excitation purity (see 9.1.4), p e , by the equation 

Pc = PeYd // (9.2) 

where y d and y are the y-chromaticity coordinates, respectively, of the monochromatic 
stimulus and the colour stimulus considered. 

Note 3: In the CIE 1964 standard colorimetric system, the colorimetric purity, p c , 10 is defined 
by the relation given in Note 2, but using p eil0 , ycuo, and y 10 instead of p e , y d , and y 

9. 1.4 Excitation purity p e 

Quantity, p e , defined by the ratio NCIND of two collinear distances on the chromaticity 
diagram of the CIE 1931 or 1964 standard colorimetric system, the first distance being that 
between the point C representing the colour stimulus considered and the point N representing 
the specified achromatic stimulus; the second distance being that between the point N and 
the point D on the spectrum locus at the dominant wavelength of the colour stimulus 
considered. The definition leads to the following expressions: 

p IzLl. or p e =±zln- (9.3) 

Yd-Vn ><d-Xn 

where (x, y), (x n , y n ), (x d , y d ) are the x, y chromaticity coordinates of the points C, N and D, 
respectively. 

Note 1: For colour stimuli for which no dominant wavelength exists, see Note 1 under 
colorimetric purity (Section 9.1.3). 



22 



CI E 15:2004 



Note 2: The formulae in x and y are equivalent but the use of that which has the greater value 
in the numerator results in greater precision. 

Note 3: Excitation purity is related to colorimetric purity by the equation: 

Pe = Pc ylVt, Or Pe.10 = Pc.10 VvJYw 

9.2 Special metamerism indices 20 

Two specimens having identical tristimulus values for a given reference illuminant and 
reference observer are metameric if their spectral radiance distributions differ within the 
visible spectrum. The procedures concerned with a special metamerism index for a change 
from a reference illuminant to a test illuminant of different spectral composition, or that for a 
change from a reference observer to a test observer of different colour-matching functions are 
called the determination of special metamerism indices. 

A measure of the metamerism for the two specimens is the colour difference between 
the two metameric specimens caused by substituting an illuminant, "special metamerism 
index: change in illuminant", and caused by substituting an observer, "special metamerism 
index: change in observer". The colour difference is evaluated using a CIE colour difference 
formula and it must be clearly stated which formula has been used. 

It is recommended that for two specimens whose corresponding tristimulus values 
(Xi - X 2 , Yi = Y 2 , Zi = Z 2 ) are identical with respect to a reference illuminant and observer, 
the metamerism index, M, be set equal to the colour difference A£* ab between the two 
specimens computed for the test illuminant or for the test observer. 

9.2. 1 Special metamerism index: change in iliuminant 

This procedure defines a special metamerism index M itm for a change from a reference 
illuminant to a test illuminant of different spectral composition. 

Note: The metamerism index M j!m is not suitable for determining the resultant colour shift or 
specifying the colour constancy of a single object colour when the illuminant is 
changed. 

9.2.1 .1 Tristimulus values under reference illuminant 

For a pair of metameric object colours, their tristimulus values X rh Y Ti} Z r/ (/" = 1, 2) under a 
reference illuminant are computed by the usual CIE recommendation (see Section 7) as 



(9.4) 



for m-r (reference illuminant), where p t (X) is the spectral reflectance of the metameric pair 
( / = 1 , 2), S(a) is the spectral power distribution of the reference illuminant, and x(Z) , y{X) , 

z{a) are the colour-matching functions of either the CIE 1931 or 1964 standard colorimetric 
observers. It should be stated which observer has been used, and 

100 

(9.5) 



X m ,i 


X 


P A) S(X) 


x(X) AX 


' m,i 


A 


p{X) S(X) y(X) AX 


^■m,i ' 


=*z 


PkX) S(^) 


z(X) AX 



X 

The preferred reference illuminant is CIE standard illuminant D65. If another 
illuminant is used as reference, this should be noted. 

For the set of the tristimulus values X Tih Y Xth Z rJ (/ = 1 ,2), the following relation holds by 
definition. 

x r .i=x ri2l r r ,i-y r , 2 , z n1 =z rT2 (9.6) 



23 



CIE 15:2004 



If Equ. 9.6 fails to hold exactly, a suitable account should be taken of this failure. The 
nature of such account should be completely specified and the size of the failure recorded. 
See Note 1 after 9.2.2.3. 

9.2.1 .2 Tristimulus values under test iliuminant 

For the same pair of metameric object colours, their tristimulus values X u , y M ,Z t) ,- (/ = 1, 2) 
under test iliuminant are computed from Equ. 9.4 with m~{, by inserting the spectral power 
distribution of the test iliuminant into S(X). 

Suitable test illuminants include CIE standard iliuminant A and the FL- and HP- 
illuminants defined in Table T.6 and T.7. 

The FL-illuminants represent typical fluorescent lamps 21 . Colorimetric data for these 
illuminants 3re given in Table T.8. For the colour rendering index calculation the method as 
described in CIE 13.3 (CIE, 1995b) was used. The most appropriate choice of test iliuminant 
depends upon application, but where only a few typical FL-i!luminants are to be selected, 
FL2, FL7 and FL1 1 should take priority. 

The HP-illuminants are typical high-pressure lamp spectra used at the time of 
publishing this report 22 . It may be useful to determine the metamerism index with respect to 
several test illuminants. The specific test iliuminant used must be identified as a subscript to 
M, e.g. M Aiiim orM FL11rilmi etc. 

9.2.1 .3 Colour difference and metamerism index 

The colour difference A£* ab is computed between the tristimulus values X t>1 , / u , Z u of object 
colour 1 , and X t2 , Yt, 2 > A,2 of object colour 2. Then the metamerism index M ilm is defined as 

M„ m = A£* ab (9.7) 

If colour difference formulas other than CIELAB are used, this should be noted. 

9.2.2 Special metamerism index; change in observer 

The CIE 1931 and 1964 standard colorimetric observers represent the colour vision 
properties of the average population reasonably well. Nevertheless it is well known that 
individual deviations in the colour-matching functions occur among colour normal observers. 

The special metamerism index: change in observer (CIE, 1989) was introduced to 
describe the average degree of mismatch found among metameric colours if the colour- 
matching functions of one of the standard colorimetric observers are changed to those of a 
standard deviate observer of normal colour vision. 

9.2.2.1 Tristimulus values for standard colorimetric observers 

For a pair of metameric object colours, their tristimulus values X Uh Y ,Z tJ (i ~ 1, 2) for the 
standard colorimetric (reference) observers are computed from Equ. 9.4, with n7=r, by use of 
either the CIE 1 931 or 1 964 colour-matching functions. 

If the two metameric object colours fail to be a precise match with respect to the 
standard colorimetric observer, a suitable account should be taken of this failure. The nature 
of such account should be completely specified and the size of the failure recorded. See Note 
1 after 9.2.2.3. 

9.2.2.2 Tristimulus values for standard deviate observer 

For the same pair of metameric object colours, their tristimulus values X u , Y t;h Z tJ (i - 1 , 2) for 
the standard deviate (test) observer are computed from Equ. 9.4, with rn=t, by inserting the 
colour-matching functions x 6 {A), y 6 {A), z d (i) of the standard deviate observer. The colour- 
matching functions x d (A), y d (/L), z d (2)are given by 



24 



CIE 15:2004 
x d (A)= x(A) + Ax(2) 

y d W= yW + Ayw (9.8) 

z d (A)= z(A) + AzU) 

where Ax(^) , Ay (A) , Az(A) are the so-called first deviation functions defined in Table 1.1 of 
(CIE, 1989) and are reproduced in Table T.10. 

9.2.2.3 Colour difference and metamerism index 

The colour difference AE* ab is computed between the tristimulus values X t> i, Y t ,i> Zt,i of object 
colour 1 , and X ti2 , Y ti2l Z ti2 of object colour 2. Then the metamerism index M obs is defined as 

M ob5 = AE* ab (9.9) 

If a colour difference formula other than CIELAB is used, this should be included in 
the parenthesis as e.g. M obs (u*v*). 

Notes on special metamerism indices 

Note 1 : When the samples are not exactly metameric, that is X r1 ^ X r>2 , Y r>1 ^ Y r;2) 
Z r1 ^Z r2 , then the tristimulus values X t2 , Y t2 , Z t2 are adjusted by the multiplicative 
method as follows. 

X\,2 ~ ^t,2 (Ka I X r2 ), Y' t ,2 = Y t)2 ( Yr.1 ' Y ri2 ), Z' t 2 = Z t ,2 (^r,1 ' ^2) (9.1 0) 

Note 2: Each colour normal observer shows a colour difference AE*, for a sample pair 
metameric with respect to a reference observer and an irradiating illuminant. About 
95 % of APs for colour normal observers are usually found to be within 2 AM obs (a*b* 
or u*v*). 

Note 3: Further characterization of the observer metamerism can be done by calculating the 
range of colour mismatch, see (CIE, 1989). 

9.3 Assessment of the quality of a daylight simulator for coiorimetry 23 

The quality of simulators of CIE daylight illuminants D50, D55, D65 and D75 can be assessed 
by calculating the special metamerism index for change in illuminant, employing specified 
samples that are metameric matches for the CIE illuminants D50, D55, D65 and D75, 
respectively, and the CIE 1964 standard colorimetric observer. The purpose of this 
assessment is to quantify the suitability of a test source as a practical reproduction of CIE 
standard illuminant D50, D55, D65, or D75for colorimetric tasks 24 . 

The basis for the assessment is the special metamerism index: change in illuminant 
(see Section 9.2.1), employing specified samples that are metameric matches for the 
standard daylight illuminant and the CIE 1964 standard colorimetric observer. The method 
quantifies the mismatch resulting when samples that are a match under the standard daylight 
illuminant are viewed under the illumination of the test source, the CIE 1964 standard 
colorimetric observer being used throughout. 

A visible range metamerism index is employed to evaluate the colorimetric suitability 
of the test source for the visible wavelength range. Tables of spectral reflection radiance 
factor define the metameric samples. 

An ultraviolet range metamerism index is employed with a second set of metameric 
samples to evaluate the suitability of the test source in relation to ultraviolet-excited 
luminescent colours. The metameric sample pairs for this assessment are comprised of a 
luminescent and a non-luminescent sample, which are spectrally identical matches for the 
standard daylight illuminant. The non-luminescent sample in each metameric pair is specified 
by values of spectral reflection radiance factor for each standard daylight illuminant (D50, 
D55, D65, and D75). 



25 



CIE 15:2004 



The luminescent sample in each metameric pair is specified by values of spectral 
reflection radiance factor, relative spectral distribution of radiance emitted by fluorescence, 
and spectral external radiant efficiency. 

The ultraviolet range metamerism index quantifies the failure of the spectrally 
identical match between the luminescent and the non-luminescent sample pairs resulting 
from changing the illuminating source from a standard daylight illuminant to a test source. 

Detailed description of the test method, including the tables needed for calculating 
the quality index, and a computer program of the calculation method on disk, are published in 
CIE 51.2-1999 (CIE, 1999c), see also (CIE, 2001b). 

9.4 The evaluation of whiteness 25 

To promote uniformity of practice in the evaluation of whiteness of surface colours, it is 
recommended that the formulae for whiteness, IV or W 10j and for tint, T w or 7" W|10 , given below, 
be used for comparisons of the whiteness of samples evaluated for CIE standard illuminant 
D65. The application of the formulae is restricted to samples that are called "white" 
commercially, that do not differ much in colour and fluorescence, and that are measured on 
the same instrument at nearly the same time. Within these restrictions, the formulae provide 
relative, but not absolute, evaluations of whiteness, that are adequate for commercial use, 
when employing measuring instruments having suitable modern and commercially available 
facilities. 

W = Y + 800(x n - x) + 1 700(y n - y) 

W10 = Vio + 800(x ni10 -x 10 ) + 1700(y ni1 o-yio) (9.11) 

Tw = 1000(x n -x)-650(y n -y) 

7"w,io = 900(x n , 10 ~x 10 )-650(y n , 10 -yio) 

where Y is the V-tristimulus value of the sample, x and y are the x, y chromaticity coordinates 
of the sample, and x n , y n are the chromaticity coordinates of the perfect diffuser, all for the 
CIE 1931 standard colorimetric observer; Y 10l x 10 , yio, x n ,io and y ni10 are similar values for the 
CIE 1964 standard colorimetric observer. 

Note 1: The higher the value of Wot i/V 10 , the greater is the indicated whiteness. The more 
positive the value of T w or 7 w10j the greener the tint; the more negative the value of T w 
or T w10 , the redder the tint. For the perfect diffuser W and LV 10 are equal to 100, and 
T w and T W)10 are equal to zero. 

Note 2: Linear whiteness formulae are applicable only within a restricted volume of the colour 
solid. These formulae may be used only for samples whose values of W or 1/V 10 and 
T w or T w>10 lie within the following limits: 

Wot W 1Q greater than 40 and less than 5Y- 280, or 5Y 10 - 280; 

7" w or 7" W|10 greater than -4 and less than +2. 

Note 3: The tint formulae are based on the empirical results that lines of equal tint run 
approximately parallel to lines of dominant wavelength 466 nm in the x, y and x 10 , yio 
chromaticity diagrams. 

Note 4: Equal differences in Wot W w do not always represent equal perceptual differences in 
whiteness, nor do equal differences in 7 W or T w10 always represent equal perceptual 
differences in greenishness or reddishness of whites. Measures of whiteness and tint 
that correlate uniformly with these perceptual attributes would require more 
complicated formulae, which is beyond present knowledge. 

9.5 Calculation of correlated colour temperature 26 

The concept of correlated colour temperature used to be based on visual observations. 
Recent investigations have shown (see Borbely et al., 2001) that no metrological definition 
can be based on such perceptual investigations. Therefore a new definition has been 
proposed. The definition agrees with the previously recommended calculation method and 
thus does not cause any changes to calculated values. 



26 



CiE 15:2004 



correlated colour temperature (7 cp ) 

temperature of a Pianckian radiator having the chromaticity nearest the chromaticity 
associated with the given spectral distribution on a diagram where the (CIE 1931 standard 
observer based) u\ 2/3v' coordinates of the Pianckian locus xm and the test stimulus are 
depicted 

Note 1 : The concept of correlated colour temperature should not be used if the chromaticity of 

the test source differs more than AC = [(u\-u' P ) 2 + i.*(v' t -v' P ) 2 ] 1/2 = 5-10" 2 from the 

9 

Pianckian radiator, where u\,v\ refer to the test source, u' P y P to the Pianckian 

radiator. 

Note 2: Correlated colour temperature can be calculated by a simple minimum search 
computer program that searches for that Pianckian temperature that provides the 
smallest chromaticity difference between the test chromaticity and the Pianckian 
locus, or e.g. by a method recommended by Robertson (1968). 



10. REFERENCES 

ALMAN, D.H., BSLLMEYER, F.W. JR., 1976. Integrating sphere errors in the colorimetry of 
fluorescent materials. Color Res. Appl., 1, 141-145, 1976. 

ASTM, 1999. American Society for Testing and Materials Standard E 308. Standard practice 
for computing the colors of objects by using the CiE system, 1999. 

ASTM, 2001. American Society for Testing and Materials E-2022-01. Standard practice for 
calculation of weighting factors for tristimulus integration, 2001 . 

ASTM, 2003. American Society for Testing and Materials Standard E2022-01. Standard 
practice for calculating of weighting factors for tristimulus integration, 2003. see e.g. ASTM 
Book of Standards Vol. 06.01 

BORBELY, A., SAMSON, A., SCHANDA, J., 2001. The concept of correlated colour 
temperature revisited. Color Res. Appl., 28/6, 450-457, 2001. 

CIE, 1931. Proc. of the 8th Session of CIE, Cambridge, 19-29, 1931. 

CIE, 1948. Proc. of the 11th Session of CIE, Paris, 16, 1948. 

CIE, 1951. Proc. of the 12th Session of CiE, Stockholm, Vol. 3, 63, 1951. 

CIE, 1955. Proc. of the 13th Session of CIE, Zurich, Vol. 1, Section 1.3.1, 12-13, 1955. 

CIE, 1957. CIE Bulletin No. 3, 16, 1957. 

CIE, 1959. Proc. of the 14th Session of CIE, Brussels, Vol. A, 91-109, 1959. 

CIE, 1963. Proc. of the 15th Session of CIE, Vienna, Vol. A, 35, 1963. 

CIE, 1967. Proc. of the 16th Session of CiE, Washington, D.C., Vol. A, 95-97, 1967. 

CIE, 1971. CIE 15-1971. Colorimetry, 1971. 

CIE, 1972. Supplement No. 1 to CIE 15-1971 Special metamerism index: Change in 
illuminant, 1972. 

CIE, 1978. Supplement No. 2 to CIE 15-1971. Recommendations on uniform colour spaces, 
colour-difference equations, psychometric colour terms, 1978. 

CIE, 1979a. CIE 44-1979. Absolute methods for reflection measurements, 1979. 

CiE, 1979b. CIE 46-1979. A review of publications on properties and reflection values of 
material reflection standards, 1979. 



XIM In calculating the chromaticity coordinates of the Pianckian radiator the c 2 value according 
to ITC-90 has to be used (c 2 = 1 ,4388) in Planck's equation for standard air, but assuming 
n=1. See Appendix E. 



27 



CIE 15:2004 



CIE, 1981. CIE 51-1981. A method for assessing the quality of daylight simulators for 
coiorimetry, 1981. 

CIE, 1986a. CiE S002-1986. CIE standard colorimetric observers, 1986. (Published also as 
C IE/ISO 10527:1991). 

CIE, 1986b. CIE 15.2-1986. Coiorimetry, Second Edition, 1986. 

CIE, 1987. CIE 17.4-1987. International Lighting Vocabulary, 1987. 

CIE, 1988. CIE 76-1988. Intercomparison on measurement of (total) spectral radiance factor 
of luminescent specimens, 1988. 

CIE, 1989. CIE 80-1989. Special metamerism index: Change in observer, 1989. 

CIE, 1993. CIE 101-1993. Parametric effects in colour difference evaluation, 1993. 

CIE, 1995a. CIE 116-1995. Industrial colour difference evaluation, 1995. 

CIE, 1995b. CIE 13.3-1995. Method of measuring and specifying colour rendering properties 
of light sources, 1995. 

CIE, 1998a. CiE 131-1998. The CIE 1997 interim colour appearance model (simple version), 
CIECAM97S, 1998. 

CIE, 1998b. CIE x014-1998. Proc. of the CiE expert symposium '97 on colour standards for 
imaging technology, 1998. 

CIE, 1998c. Standard CiE S005/E-1998. CIE standard illuminants for coiorimetry, 1998. 
(Published also as ISO 10526/CIE S 005/E-1999). 

CIE, 1998d. CIE 130-1998. Practical methods for the measurement of reflectance and 
transmittance, 1998. 

CIE, 1999a. CiE 135/4-1999. Some recent developments in colour difference evaluation, 
1999. 

CiE, 1999b. CIE 135/3-1999. Supplement 1-1999 to CIE 51-1981, Virtual metamers for 
assessing the quality of simulators of CIE illuminant D50, 1999. 

CIE, 1999c. CIE 51.2-1999. A method for assessing the quality of daylight simulators for 
coiorimetry, 1999. 

CIE, 2001 a. CiE 1 42-2001 . Improvement to industrial colour-difference evaluation, 2001 . 

CIE, 2001b. CIE DS 012:2001 . Standard method of assessing the spectral quality of daylight 
simulators for visual appraisal and measurement of colour, 2001 . 

CIE, 2004a. CIE DS 014-2.2:2004 Coiorimetry- Part 2: CIE Standard Illuminants, 2004. 

CIE, 2004b. CIE 159:2004. A colour appearance model for colour management systems: 
CIECAM02, 2004. 

DIN, 2003. DIN 6176:2003. Colorimetric determination of colour differences of surface colours 
using the DIN 99 formula, 2003. 

FAIRMAN, H.S., 1985. The calculation of weight factors for tristimulus integration. Color Res, 
AppL, 10, 199-203, 1985. 

GUNDLACH, D., MALLWiTZ, E., 1976. Fragen der Probenbeleuchtung und MeSgeometrie in 
der Farbmessung. Die Farbe : 25, 1 13-130, 1976. 

JIS, 1991. JIS 8716. Fluorescent lamp as a simulator of CIE standard illuminant D 65 for a 
visual comparison of surface colours - Type and characteristics, 1991 . 

JUDD, D.B., MACADAM, D.L, WYSZECKI, G., 1964. with the collaboration of BUDDE, H.W., 
CONDIT, H.R., HENDERSON, ST., SIMONDS, J.L. Spectral distribution of typical daylight as 
a function of correlated color temperature. J. Opt. Soc. Am. 54, 1031-1040, 1964. 

LE GRAND, Y., 1968. Light, Colour and Vision. Second Edition. London, Chapman and Hall, 
1-564, 1968. 



28 



CI E 15:2004 



Li, C.J., LUO, M.R., R!GG, B., 2004. A new method for computing optimum weights for 
calculating CIE Tristimulus Values. Color Res. AppL, 29, 91-103, 2004. 



MCLAREN, K., 1980. CIELAB hue-angle anomalies at low tristimulus ratios. Color Res. AppL, 
5, 139-143, 1980. 

PAULI, H, 1976. Proposed extension of the CIE recommendation on "Uniform color spaces, 
color difference equations, and metric color terms". J. Opt. Soc. Am., 66, 866-867, 1976. 

ROBERTSON, A.R., 1968. Computation of correlated color temperature and distribution 
temperature. J. Opt Soc. Am., 58, 1528-35, 1968. 

ROBERTSON, A.R., 1978. CIE guidelines for coordinated research on colour difference 
evaluation. Color Res. AppL, 3, 149-151, 1978. 

SEVE, R., 1991. New formula for the computation of CiE 1976 hue difference. Color Res. 
AppL, 16, 217-218, 1991. 

SEVE, R., 1996. Practical formula for the computation of CIE 1976 hue difference. Color Res. 
AppL, 21, 314, 1996. 

SEVE, R., DUVAL, B., 2003. Interpolation procedure: Proposals and comments. In CIE 
152:2003, Proc. CIE 25 th Session Vol. 1. D1 -74-77, 2003. 

STOKES, M., BRILL, M.H., 1992. Efficient computation of AH* ab . Color Res. AppL, 17, 410- 
411, 1992. 

VENABLE, W.H., 1989. Accurate tristimulus values from spectral data. Color Res. AppL, 14, 
260-267, 1989. 

WYSZECKi, G., 1968. Recent agreements reached by the Colorimetry Committee of the 
Commission Internationale de i'Eclairage, J. Opt. Soc. Am., 58, 290-292, 1968. 

WYSZECKI, G., STILES, W.S., 1982. Color Science - Concepts and Methods, Quantitative 
Data and Formulae. 2nd Edition. New York, John Wiley & Sons, 1982. 



29 



C!E 15:2004 



11. 



TABLES 



This Section of the report contains tables of abridged and truncated coiorimetric data. The full 
tables - recommended for genera! use - are found in the CIE standards on co!orimetry xlv 
The tables presented here are intended for use, only when the highest precision is not 
required. Users should check before using these tables whether the level of precision meets 
their needs. 

The iiluminant tables in this section are provided for the range between 300 nm and 
780 nm. The tables of other coiorimetric functions are provided for the range between 380 nm 
and 780 nm. All tables are at 5 nm intervals. 

11.1 Table T.1. Relative spectral power distributions of CIE illuminants 

Relative spectral power distributions [S(A)] of CIE standard illuminants A and D65, as well as 
CIE illuminants C, D50, D55 and D75 for wavelengths X = 300 nm to 780 nm at 5 nm 
intervais xv 



A, nm 


Standard 

Iiluminant A 


Standard 
iiluminant D65 


Iiluminant 
C 


Iiluminant 
D50 


Iiluminant 
D55 


Iiluminant 
D75 


300 


0,930 483 


0,034 100 


0,00 


0,019 


0,024 


0,043 


305 


1,12821 


1 ,664 30 


0,00 


1,035 


1,048 


2,588 


310 


1,357 69 


3,294 50 


0,00 


2,051 


2,072 


5,133 


315 


1,622 19 


11,765 2 


0,00 


4,914 


6,648 


17,470 


320 


1,925 08 


20,236 


0,01 


7,778 


1 1 ,224 


29,808 


325 


2,269 80 


28,644 7 


0,20 


11,263 


15,936 


42,369 


330 


2,659 81 


37,053 5 


0,40 


14,748 


20,647 


54,930 


335 


3,098 61 


38,501 1 


1,55 


16,348 


22,266 


56,095 


340 


3,589 68 


39,948 8 


2,70 


17,948 


23,885 


57,259 


345 


4,136 48 


42,430 2 


4,85 


19,479 


25,851 


60,000 


350 


4,742 38 


44,91 1 7 


7,00 


21,010 


27,817 


62,740 


355 


5,410 70 


45,775 


9,95 


22,476 


29,219 


62,861 


360 


6,144 62 


46,638 3 


12,90 


23,942 


30,621 


62,982 


365 


6,947 20 


49,363 7 


17,20 


25,451 


32,464 


66,647 


370 


7,821 35 


52,089 1 


21,40 


26,961 


34,308 


70,312 


375 


8,769 80 


51,032 3 


27,50 


25,724 


33,446 


68,507 


380 


9,795 10 


49,975 5 


33,00 


24,488 


32,584 


66,703 


385 


10,899 6 


52,311 8 


39,92 


27,179 


35,335 


68,333 


390 


12,085 3 


54,648 2 


47,40 


29,871 


38,087 


69,963 


395 


13,354 3 


68,701 5 


55,17 


39,589 


49,518 


85,946 


400 


14,708 


82,754 9 


63,30 


49,308 


60,949 


101,929 


405 


16,148 


87,120 4 


71,81 


52,910 


64,751 


106,911 


410 


17,675 3 


91,486 


80,60 


56,513 


68,554 


111,894 


415 


19,290 7 


92,458 9 


89,53 


58,273 


70,065 


112,346 


420 


20,995 


93,431 8 


98,10 


60,034 


71,577 


112,798 



XIV These tables can also be found on the accompanying CD-ROM. 

xv Standard iiluminant A and standard iiluminant D65 data are every fifth value from the CIE 
Standard. The iiluminant C data are unchanged from CIE 15.2-1986. The D50, D55 and D75 
data are calculated according to the present version of CIE 15. 



30 



CiE 15:2004 



X, nm 


Standard 
Illuminant A 


Standard 
Illuminant D65 


Illuminant 
C 


Illuminant 
D50 


Illuminant 
D55 


Illuminant 
D75 


425 


22,788 3 


90,057 


105,80 


58,926 


69,746 


107,945 


430 


24,670 9 


86,682 3 


112,40 


57,818 


67,914 


103,092 


435 


26,642 5 


95,773 6 


117,75 


66,321 


76,760 


112,145 


440 


28,702 7 


104,865 


121,50 


74,825 


85,605 


121,198 


445 


30,850 8 


110,936 


123,45 


81,036 


91,799 


127,104 


450 


33,085 9 


117,008 


124,00 


87,247 


97,993 


133,010 


455 


35,406 8 


117,410 


123,60 


88,930 


99,228 


132,682 


460 


37,812 1 


117,812 


123,10 


90,612 


100,463 


132,355 


465 


40,300 2 


116,336 


123,30 


90,990 


100,188 


129,838 


470 


42,869 3 


114,861 


123,80 


91,368 


99,913 


127,322 


475 


45,517 4 


115,392 


124,09 


93,238 


101,326 


127,061 


480 


48,242 3 


115,923 


123,90 


95,109 


102,739 


126,800 


485 


51,041 8 


112,367 


122,92 


93,536 


100,409 


122,291 


490 


53,913 2 


108,811 


120,70 


91,963 


98,078 


117,783 


495 


56,853 9 


109,082 


116,90 


93,843 


99,379 


117,186 


500 


59,861 1 


109,354 


112,10 


95,724 


100,680 


116,589 


505 


62,932 


108,578 


106,98 


96,169 


100,688 


115,146 


510 


66,063 5 


107,802 


102,30 


96,613 


100,695 


113,702 


515 


69,252 5 


106,296 


98,81 


96,871 


100,341 


111,181 


520 


72,495 9 


104,790 


96,90 


97,129 


99,987 


108,659 


525 


75,790 3 


106,239 


96,78 


99,614 


102,098 


109,552 


530 


79,132 6 


107,689 


98,00 


102,099 


104,210 


110,445 


535 


82,519 3 


106,047 


99,94 


101,427 


103,156 


108,367 


540 


85,947 


104,405 


102,10 


100,755 


102,102 


106,289 


545 


89,412 4 


104,225 


103,95 


101,536 


102,535 


105,596 


550 


92,912 


104,046 


105,20 


102,317 


102,968 


104,904 


555 


96,442 3 


102,023 


105,67 


101,159 


101,484 


102,452 


560 


100,000 


100,000 


105,30 


100,000 


100,000 


100,000 


565 


103,582 


98,167 1 


104,11 


98,868 


98,608 


97,808 


570 


107,184 


96,334 2 


102,30 


97,735 


97,216 


95,616 


575 


110,803 


96,061 1 


100,15 


98,327 


97,482 


94,914 


580 


114,436 


95,788 


97,80 


98,918 


97,749 


94,213 


585 


118,080 


92,236 8 


95,43 


96,208 


94,590 


90,605 


590 


121,731 


88,685 6 


93,20 


93,499 


91,432 


86,997 


595 


125,386 


89,345 9 


91,22 


95,593 


92,926 


87,112 


600 


129,043 


90,006 2 


89,70 


97,688 


94,419 


87,227 


605 


132,697 


89,802 6 


88,83 


98,478 


94,780 


86,684 


610 


136,346 


89,599 1 


88,40 


99,269 


95,140 


86,140 


615 


139,988 


88,648 9 


88,19 


99,155 


94,680 


84,861 


620 


143,618 


87,698 7 


88,10 


99,042 


94,220 


83,581 


625 


147,235 


85,493 6 


88,06 


97,382 


92,334 


81,164 


630 


150,836 


83,288 6 


88,00 


95,722 


90,448 


78,747 



31 



CIE 15:2004 



X, nm 


Standard 
llluminant A 


Standard 
llluminant D65 


llluminant 
C 


llluminant 
D50 


llluminant 
D55 


llluminant 
D75 


635 


154,418 


83,493 9 


87,86 


97,290 


91,389 


78,587 


640 


157,979 


83,699 2 


87,80 


98,857 


92,330 


78,428 


645 


161,516 


81,863 


87,99 


97,262 


90,592 


76,614 


650 


165,028 


80,026 8 


88,20 


95,667 


88,854 


74,801 


655 


168,510 


80,120 7 


88,20 


96,929 


89,586 


74,562 


660 


171,963 


80,214 6 


87,90 


98,190 


90,317 


74,324 


665 


175,383 


81,246 2 


87,22 


100,597 


92,133 


74,873 


670 


178,769 


82,277 8 


86,30 


103,003 


93,950 


75,422 


675 


182,118 


80,281 


85,30 


101,068 


91,953 


73,499 


680 


185,429 


78,284 2 


84,00 


99,133 


89,956 


71,576 


685 


188,701 


74,002 7 


82,21 


93,257 


84,817 


67,714 


690 


191,931 


69,721 3 


80,20 


87,381 


79,677 


63,852 


695 


195,118 


70,665 2 


78,24 


89,492 


81,258 


64,464 


700 


198,261 


71,609 1 


76,30 


91,604 


82,840 


65,076 


705 


201,359 


72,979 


74,36 


92,246 


83,842 


66,573 


710 


204,409 


74,349 


72,40 


92,889 


84,844 


68,070 


715 


207,411 


67,976 5 


70,40 


84,872 


77,539 


62,256 


720 


210,365 


61,604 


68,30 


76,854 


70,235 


56,443 


725 


213,268 


65,744 8 


66,30 


81,683 


74,768 


60,343 


730 


216,120 


69,885 6 


64,40 


86,511 


79,301 


64,242 


735 


218,920 


72,486 3 


62,80 


89,546 


82,147 


66,697 


740 


221,667 


75,087 


61,50 


92,580 


84,993 


69,151 


745 


224,361 


69,339 8 


60,20 


85,405 


78,437 


63,890 


750 


227,000 


63,592 7 


59,20 


78,230 


71,880 


58,629 


755 


229,585 


55,005 4 


58,50 


67,961 


62,337 


50,623 


760 


232,115 


46,418 2 


58,10 


57,692 


52,793 


42,617 


765 


234,589 


56,611 8 


58,00 


70,307 


64,360 


51,985 


770 


237,008 


66,805 4 


58,20 


82,923 


75,927 


61,352 


775 


239,370 


65,094 1 


58,50 


80,599 


73,872 


59,838 


780 


241,675 


63,382 8 


59,10 


78,274 


71,818 


58,324 



32 



CI E 15:2004 



1 1 .2 Table T\2> Components S (A), S^A), S 2 (/l) 

Components S Q (X), Si(A), S 2 (A) of daylight used in the calculation of relative spectral power 
distributions of CIE daylight illuminants of different correlated colour temperatures, for 
wavelengths X = 300 nm to 830 nm at 5 nm intervals. 



A, nm 


S (A) 


Si(A) 


S 2 (A) 


300 


0,04 


0,02 


0,00 


305 


3,02 


2,26 


1,00 


310 


6,00 


4,50 


2,00 


315 


17,80 


13,45 


3,00 


320 


29,60 


22,40 


4,00 


325 


42,45 


32,20 


6,25 


330 


55,30 


42,00 


8,50 


335 


56,30 


41,30 


8,15 


340 


57,30 


40,60 


7,80 


345 


59,55 


41,10 


7,25 


350 


61,80 


41,60 


6,70 


355 


61,65 


39,80 


6,00 


360 


61,50 


38,00 


5,30 


365 


65,15 


40,20 


5,70 


370 


68,80 


42,40 


6,10 


375 


66,10 


40,45 


4,55 


380 


63,40 


38,50 


3,00 


385 


64,60 


36,75 


2,10 


390 


65,80 


35,00 


1,20 


395 


80,30 


39,20 


0,05 


400 


94,80 


43,40 


-1,10 


405 


99,80 


44,85 


-0,80 


410 


104,80 


46,30 


-0,50 


415 


105,35 


45,10 


-0,60 


420 


105,90 


43,90 


-0,70 


425 


101,35 


40,50 


-0,95 


430 


96,80 


37,10 


-1,20 


435 


105,35 


36,90 


-1,90 


440 


113,90 


36,70 


-2,60 


445 


119,75 


36,30 


-2,75 


450 


125,60 


35,90 


-2,90 


455 


125,55 


34,25 


-2,85 


460 


125,50 


32,60 


-2,80 


465 


123,40 


30,25 


-2,70 


470 


121,30 


27,90 


-2,60 


475 


121,30 


26,10 


-2,60 


480 


121,30 


24,30 


-2,60 


485 


117,40 


22,20 


-2,20 



X, nm 


S (A) 


SiW) 


S 2 {X) 


490 


113,50 


20,10 


-1,80 


495 


113,30 


18,15 


-1,65 


500 


113,10 


16,20 


-1,50 


505 


111,95 


14,70 


-1,40 


510 


110,80 


13,20 


-1,30 


515 


108,65 


10,90 


-1,25 


520 


106,50 


8,60 


-1,20 


525 


107,65 


7,35 


-1,10 


530 


108,80 


6,10 


-1,00 


535 


107,05 


5,15 


-0,75 


540 


105,30 


4,20 


-0,50 


545 


104,85 


3,05 


-0,40 


550 


104,40 


1,90 


-0,30 


555 


102,20 


0,95 


-0,15 


560 


100,00 


0,00 


0,00 


565 


98,00 


-0,80 


0,10 


570 


96,00 


-1,60 


0,20 


575 


95,55 


-2,55 


0,35 


580 


95,10 


-3,50 


0,50 


585 


92,10 


-3,50 


1,30 


590 


89,10 


-3,50 


2,10 


595 


89,80 


-4,65 


2,65 


600 


90,50 


-5,80 


3,20 


605 


90,40 


-6,50 


3,65 


610 


90,30 


-7,20 


4,10 


615 


89,35 


-7,90 


4,40 


620 


88,40 


-8,60 


4,70 


625 


86,20 


-9,05 


4,90 


630 


84,00 


-9,50 


5,10 


635 


84,55 


-10,20 


5,90 


640 


85,10 


-10,90 


6,70 


645 


83,50 


-10,80 


7,00 


650 


81,90 


-10,70 


7,30 


655 


82,25 


-11,35 


7,95 


660 


82,60 


-12,00 


8,60 


665 


83,75 


-13,00 


9,20 


670 


84,90 


-14,00 


9,80 


675 


83,10 


-13,80 


10,00 



33 



CIE 15:2004 



A, nm 


SoU) 


Si(A) 


S 2 (A) 


680 


81,30 


-13,60 


10,20 


685 


76,60 


-12,80 


9,25 


690 


71,90 


-12,00 


8,30 


695 


73,10 


-12,65 


8,95 


700 


74,30 


-13,30 


9,60 


705 


75,35 


-13,10 


9,05 


710 


76,40 


-12,90 


8,50 


715 


69,85 


-11,75 


7,75 


720 


63,30 


-10,60 


7,00 


725 


67,50 


-11,10 


7,30 


730 


71,70 


-11,60 


7,60 


735 


74,35 


-11,90 


7,80 


740 


77,00 


-12,20 


8,00 


745 


71,10 


-11,20 


7,35 


750 


65,20 


-10,20 


6,70 


755 


56,45 


-9,00 


5,95 


760 


47,70 


-7,80 


5,20 



A, nm 


SoW 


Sitf) 


S 2 (A) 


765 


58,15 


-9,50 


6,30 


770 


68,60 


-11,20 


7,40 


775 


66,80 


-10,80 


7,10 


780 


65,00 


-10,40 


6,80 


785 


65,50 


-10,50 


6,90 


790 


66,00 


-10,60 


7,00 


795 


63,50 


-10,15 


6,70 


800 


61,00 


-9,70 


6,40 


805 


57,15 


-9,00 


5,95 


810 


53,30 


-8,30 


5,50 


815 


56,10 


-8,80 


5,80 


820 


58,90 


-9,30 


6,10 


825 


60,40 


-9,55 


6,30 


830 


61,90 


-9,80 


6,50 



34 



CIE 15:2004 



1 1 .3 Table T.3. Tristimuius values, chromaticity coordinates of CIE illuminants 

Tristimulus values, X, V, Z, and chromaticity coordinates x, y, and u\ v' for CIE standard 
illuminants A and D65, as well as for CIE iiluminants C, D50, D55 and D75 computed for the 
1931 and 1964 standard colorimetric observers. 

1. For the CIE 1931 standard colorimetric observer as defined in Table T.4 and illuminants 
as defined in Table T.1 (5 nm intervals over the range 380 nm to 780 nm). 





Standard 
llluminant A 


Standard 

llluminant 

D65 


llluminant 
C 


llluminant 
D50 


llluminant 
D55 


llluminant 
D75 


X 


109,85 


95,04 


98,07 


96,42 


95,68 


94,97 


Y 


100,00 


100,00 


100,00 


100,00 


100,00 


100,00 


Z 


35,58 


108,88 


118,22 


82,51 


92,14 


122,61 




X 


0,447 58 


0,312 72 


0,310 06 


0,345 67 


0,332 43 


0,299 03 


y 


0,407 45 


0,329 03 


0,316 16 


0,358 51 


0,347 44 


0,314 88 




u' 


0,255 97 


0,197 83 


0,200 89 


0,209 16 


0,204 43 


0,193 53 


V' 


0,524 29 


0,468 34 


0,460 89 


0,488 08 


0,480 75 


0,458 53 


2. For the CIE 1964 standard colorimetric observer as defined in Table T.5 and illuminants 
as defined in Table T.1 (5 nm intervals over the range 380 nm to 780 nm). 




Standard 
llluminant A 


Standard 
llluminant D65 


llluminant 
C 


llluminant 
D50 


llluminant 
D55 


llluminant 
D75 


X10 


111,14 


94,81 


97,29 


96,72 


95,80 


94,42 


Vio 


100,00 


100,00 


100,00 


100,00 


100,00 


100,00 


Z10 


35,20 


107,32 


116,14 


81,43 


90,93 


120,64 




*10 


0,451 17 


0,313 81 


0,310 39 


0,347 73 


0,334 12 


0,299 68 


yio 


0,405 94 


0,330 98 


0,319 05 


0,359 52 


0,348 77 


0,317 40 




u'io 


0,258 96 


0,197 86 


0,200 00 


0,210 15 


0,205 07 


0,193 05 


v'w 


0,524 25 


0,469 54 


0,462 55 


0,488 86 


0,481 65 


0,460 04 



35 



CIE 15:2004 

11.4 Table T.4. CIE 1931 standard colorimetric observer 

Truncated set of colour-matching functions x(/L), y(A), z(X) and corresponding chromaticity 

coordinates x(A), y(A) for wavelengths X = 380 nm to 780 nm at 5 nm intervals, rounded to 6 
and 5 decimal places respectively. Vi 



Z, nm 


X(Z) 


yW 


zW 


x(X) 


M 


380 


0,001 368 


0,000 039 


0,006 450 


0,174 11 


0,004 96 


385 


0,002 236 


0,000 064 


0,010 550 


0,174 01 


0,004 98 


390 


0,004 243 


0,000 120 


0,020 050 


0,173 80 


0,004 92 


395 


0,007 650 


0,000 217 


0,036 210 


0,173 56 


0,004 92 


400 


0,014 310 


0,000 396 


0,067 850 


0,173 34 


0,004 80 


405 


0,023 190 


0,000 640 


0,110 200 


0,173 02 


0,004 78 


410 


0,043 510 


0,001 210 


0,207 400 


0,172 58 


0,004 80 


415 


0,077 630 


0,002 180 


0,371 300 


0,172 09 


0,004 83 


420 


0,134 380 


0,004 000 


0,645 600 


0,171 41 


0,005 10 


425 


0,214 770 


0,007 300 


1,039 050 


0,170 30 


0,005 79 


430 


0,283 900 


0,011 600 


1,385 600 


0,168 88 


0,006 90 


435 


0,328 500 


0,016 840 


1 ,622 960 


0,166 90 


0,008 56 


440 


0,348 280 


0,023 000 


1,747 060 


0,164 41 


0,010 86 


445 


0,348 060 


0,029 800 


1,782 600 


0,161 10 


0,013 79 


450 


0,336 200 


0,038 000 


1,772 110 


0,156 64 


0,017 70 


455 


0,318 700 


0,048 000 


1,744 100 


0,150 99 


0,022 74 


460 


0,290 800 


0,060 000 


1,669 200 


0,143 96 


0,029 70 


465 


0,251 100 


0,073 900 


1,528 100 


0,135 50 


0,039 88 


470 


0,195 360 


0,090 980 


1,287 640 


0,124 12 


0,057 80 


475 


0,142 100 


0,112 600 


1,041 900 


0,109 59 


0,086 84 


480 


0,095 640 


0,139 020 


0,812 950 


0,091 29 


0,132 70 


485 


0,057 950 


0,169 300 


0,616 200 


0,068 71 


0,200 72 


490 


0,032 010 


0,208 020 


0,465 180 


0,045 39 


0,294 98 


495 


0,014 700 


0,258 600 


0,353 300 


0,023 46 


0,412 70 


500 


0,004 900 


0,323 000 


0,272 000 


0,008 17 


0,538 42 


505 


0,002 400 


0,407 300 


0,212 300 


0,003 86 


0,654 82 


510 


0,009 300 


0,503 000 


0,158 200 


0,013 87 


0,750 19 


515 


0,029 100 


0,608 200 


0,111 700 


0,038 85 


0,812 02 


520 


0,063 270 


0,710 000 


0,078 250 


0,074 30 


0,833 80 


525 


0,109 600 


0,793 200 


0,057 250 


0,114 16 


0,826 21 


530 


0,165 500 


0,862 000 


0,042 160 


0,154 72 


0,805 86 


535 


0,225 750 


0,914 850 


0,029 840 


0,192 88 


0,781 63 


540 


0,290 400 


0,954 000 


0,020 300 


0,229 62 


0,754 33 


545 


0,359 700 


0,980 300 


0,013 400 


0,265 78 


0,724 32 


550 


0,433 450 


0,994 950 


0,008 750 


0,301 60 


0,692 31 



XVi Chromaticity coordinates have been calculated from the non-rounded values published in 
(CIE, 1986a). 



36 



CiE 15:2004 



Z, nm 


x(X) 


VW 


Z{X) 


m 


y(A) 


555 


0,512 050 


1,000 000 


0,005 750 


0,337 36 


0,658 85 


560 


0,594 500 


0,995 000 


0,003 900 


0,373 10 


0,624 45 


565 


0,678 400 


0,978 600 


0,002 750 


0,408 74 


0,589 61 


570 


0,762 100 


0,952 000 


0,002 100 


0,444 06 


0,554 71 


575 


0,842 500 


0,915 400 


0,001 800 


0,478 77 


0,520 20 


580 


0,916 300 


0,870 000 


0,001 650 


0,512 49 


0,486 59 


585 


0,978 600 


0,816 300 


0,001 400 


0,544 79 


0,454 43 


590 


1,026 300 


0,757 000 


0,001 100 


0,575 15 


0,424 23 


595 


1,056 700 


0,694 900 


0,001 000 


0,602 93 


0,396 50 


600 


1,062 200 


0,631 000 


0,000 800 


0,627 04 


0,372 49 


605 


1,045 600 


0,566 800 


0,000 600 


0,648 23 


0,351 39 


610 


1,002 600 


0,503 000 


0,000 340 


0,665 76 


0,334 01 


615 


0,938 400 


0,441 200 


0,000 240 


0,680 08 


0,319 75 


620 


0,854 450 


0,381 000 


0,000 190 


0,691 50 


0,308 34 


625 


0,751 400 


0,321 000 


0,000 100 


0,700 61 


0,299 30 


630 


0,642 400 


0,265 000 


0,000 050 


0,707 92 


0,292 03 


635 


0,541 900 


0,217 000 


0,000 030 


0,714 03 


0,285 93 


640 


0,447 900 


0,175 000 


0,000 020 


0,719 03 


0,280 93 


645 


0,360 800 


0,138 200 


0,000 010 


0,723 03 


0,276 95 


650 


0,283 500 


0,107 000 


0,000 000 


0,725 99 


0,274 01 


655 


0,218 700 


0,081 600 


0,000 000 


0,728 27 


0,271 73 


660 


0,164 900 


0,061 000 


0,000 000 


0,729 97 


0,270 03 


665 


0,121 200 


0,044 580 


0,000 000 


0,731 09 


0,268 91 


670 


0,087 400 


0,032 000 


0,000 000 


0,731 99 


0,268 01 


675 


0,063 600 


0,023 200 


0,000 000 


0,732 72 


0,267 28 


680 


0,046 770 


0,017 000 


0,000 000 


0,733 42 


0,266 58 


685 


0,032 900 


0,011 920 


0,000 000 


0,734 05 


0,265 95 


690 


0,022 700 


0,008 210 


0,000 000 


0,734 39 


0,265 61 


695 


0,015 840 


0,005 723 


0,000 000 


0,734 59 


0,265 41 


700 


0,011 359 


0,004 102 


0,000 000 


0,734 69 


0,265 31 


705 


0,008 111 


0,002 929 


0,000 000 


0,734 69 


0,265 31 


710 


0,005 790 


0,002 091 


0,000 000 


0,734 69 


0,265 31 


715 


0,004 109 


0,001 484 


0,000 000 


0,734 69 


0,265 31 


720 


0,002 899 


0,001 047 


0,000 000 


0,734 69 


0,265 31 


725 


0,002 049 


0,000 740 


0,000 000 


0,734 69 


0,265 31 


730 


0,001 440 


0,000 520 


0,000 000 


0,734 69 


0,265 31 


735 


0,001 000 


0,000 361 


0,000 000 


0,734 69 


0,265 31 


740 


0,000 690 


0,000 249 


0,000 000 


0,734 69 


0,265 31 


745 


0,000 476 


0,000 172 


0,000 000 


0,734 69 


0,265 31 


750 


0,000 332 


0,000 120 


0,000 000 


0,734 69 


0,265 31 


755 


0,000 235 


0,000 085 


0,000 000 


0,734 69 


0,265 31 


760 


0,000 166 


0,000 060 


0,000 000 


0,734 69 


0,265 31 



37 



CIE 15:2004 



X, nm 


X(X) 


VW 


*W 


x(X) 


yW 


765 


0,000 117 


0,000 042 


0,000 000 


0,734 69 


0,265 31 


770 


0,000 083 


0,000 030 


0,000 000 


0,734 69 


0,265 31 


775 


0,000 059 


0,000 021 


0,000 000 


0,734 69 


0,265 31 


780 


0,000 042 


0,000 015 


0,000 000 


0,734 69 


0,265 31 



Summation at 5 nm intervals: 

£*P) = 21 ,371524 J^yW = 21,371327 ^W : 



21,371 540 



11.5 Table T.5. CIE 1964 standard colorimetric observer 

Truncated set of colour-matching functions x w (X), y w (A), z w (X) and chromaticity 

coordinates x 10 (A), y^{x) for wavelengths X ~ 380 nm to 780 nm at 5 nm intervals, rounded to 
6 decimal places and 5 decimal places respectively xv ". 



A,nm 


*ioU) 


yioW 


*ioW 


X 10 (/L) 


yio(^) 


380 


0,000 160 


0,000 017 


0,000 705 


0,181 33 


0,019 69 


385 


0,000 662 


0,000 072 


0,002 928 


0,180 91 


0,019 54 


390 


0,002 362 


0,000 253 


0,010 482 


0,180 31 


0,019 35 


395 


0,007 242 


0,000 769 


0,032 344 


0,179 47 


0,019 04 


400 


0,019 110 


0,002 004 


0,086 011 


0,178 39 


0,018 71 


405 


0,043 400 


0,004 509 


0,197 120 


0,177 12 


0,018 40 


410 


0,084 736 


0,008 756 


0,389 366 


0,175 49 


0,018 13 


415 


0,140 638 


0,014 456 


0,656 760 


0,173 23 


0,017 81 


420 


0,204 492 


0,021 391 


0,972 542 


0,170 63 


0,017 85 


425 


0,264 737 


0,029 497 


1,282 500 


0,167 90 


0,018 71 


430 


0,314 679 


0,038 676 


1,553 480 


0,165 03 


0,020 28 


435 


0,357 719 


0,049 602 


1,798 500 


0,162 17 


0,022 49 


440 


0,383 734 


0,062 077 


1 ,967 280 


0,159 02 


0,025 73 


445 


0,386 726 


0,074 704 


2,027 300 


0,155 39 


0,030 02 


450 


0,370 702 


0,089 456 


1,994 800 


0,151 00 


0,036 44 


455 


0,342 957 


0,106 256 


1,900 700 


0,145 94 


0,045 22 


460 


0,302 273 


0,128 201 


1,745 370 


0,138 92 


0,058 92 


465 


0,254 085 


0,152 761 


1,554 900 


0,129 52 


0,077 87 


470 


0,195 618 


0,185 190 


1,317 560 


0,115 18 


0,109 04 


475 


0,132 349 


0,219 940 


1,030 200 


0,095 73 


0,159 09 


480 


0,080 507 


0,253 589 


0,772 125 


0,072 78 


0,229 24 


485 


0,041 072 


0,297 665 


0,570 060 


0,045 19 


0,327 54 


490 


0,016 172 


0,339 133 


0,415 254 


0,020 99 


0,440 11 


495 


0,005 132 


0,395 379 


0,302 356 


0,007 30 


0,562 52 



XV!I Chromaticity coordinates have been calculated from the non-rounded values published in 
(CIE, 1986a). 



38 



CI E 15:2004 



A, nm 


X 10 (A) 


y^W 


Z 10 (A) 


X10W) 


y-ioW 


500 


0,003 816 


0,460 777 


0,218 502 


0,005 59 


0,674 54 


505 


0,015 444 


0,531 360 


0,159 249 


0,021 87 


0,752 58 


510 


0,037 465 


0,606 741 


0,112 044 


0,049 54 


0,802 30 


515 


0,071 358 


0,685 660 


0,082 248 


0,085 02 


0,816 98 


520 


0,117 749 


0,761 757 


0,060 709 


0,125 24 


0,810 19 


525 


0,172 953 


0,823 330 


0,043 050 


0,166 41 


0,792 17 


530 


0,236 491 


0,875 211 


0,030 451 


0,207 06 


0,766 28 


535 


0,304 213 


0,923 810 


0,020 584 


0,243 64 


0,739 87 


540 


0,376 772 


0,961 988 


0,013 676 


0,278 59 


0,711 30 


545 


0,451 584 


0,982 200 


0,007 918 


0,313 23 


0,681 28 


550 


0,529 826 


0,991 761 


0,003 988 


0,347 30 


0,650 09 


555 


0,616 053 


0,999 110 


0,001 091 


0,381 16 


0,618 16 


560 


0,705 224 


0,997 340 


0,000 000 


0,414 21 


0,585 79 


565 


0,793 832 


0,982 380 


0,000 000 


0,446 92 


0,553 08 


570 


0,878 655 


0,955 552 


0,000 000 


0,479 04 


0,520 96 


575 


0,951 162 


0,915 175 


0,000 000 


0,509 64 


0,490 36 


580 


1,014 160 


0,868 934 


0,000 000 


0,538 56 


0,461 44 


585 


1 ,074 300 


0,825 623 


0,000 000 


0,565 44 


0,434 56 


590 


1,118 520 


0,777 405 


0,000 000 


0,589 96 


0,410 04 


595 


1,134 300 


0,720 353 


0,000 000 


0,611 60 


0,388 40 


600 


1,123 990 


0,658 341 


0,000 000 


0,630 63 


0,369 37 


605 


1,089 100 


0,593 878 


0,000 000 


0,647 13 


0,352 87 


610 


1,030 480 


0,527 963 


0,000 000 


0,661 22 


0,338 78 


615 


0,950 740 


0,461 834 


0,000 000 


0,673 06 


0,326 94 


620 


0,856 297 


0,398 057 


0,000 000 


0,682 66 


0,317 34 


625 


0,754 930 


0,339 554 


0,000 000 


0,689 76 


0,310 24 


630 


0,647 467 


0,283 493 


0,000 000 


0,695 48 


0,304 52 


635 


0,535 110 


0,228 254 


0,000 000 


0,700 99 


0,299 01 


640 


0,431 567 


0,179 828 


0,000 000 


0,705 87 


0,294 13 


645 


0,343 690 


0,140 211 


0,000 000 


0,710 25 


0,289 75 


650 


0,268 329 


0,107 633 


0,000 000 


0,713 71 


0,286 29 


655 


0,204 300 


0,081 187 


0,000 000 


0,715 62 


0,284 38 


660 


0,152 568 


0,060 281 


0,000 000 


0,716 79 


0,283 21 


665 


0,112 210 


0,044 096 


0,000 000 


0,717 89 


0,282 11 


670 


0,081 261 


0,031 800 


0,000 000 


0,718 73 


0,281 27 


675 


0,057 930 


0,022 602 


0,000 000 


0,719 34 


0,280 66 


680 


0,040 851 


0,015 905 


0,000 000 


0,719 76 


0,280 24 


685 


0,028 623 


0,011 130 


0,000 000 


0,720 02 


0,279 98 


690 


0,019 941 


0,007 749 


0,000 000 


0,720 16 


0,279 84 


695 


0,013 842 


0,005 375 


0,000 000 


0,720 30 


0,279 70 


700 


0,009 577 


0,003 718 


0,000 000 


0,720 36 


0,279 64 


705 


0,006 605 


0,002 565 


0,000 000 


0,720 32 0,279 68 



39 



CIE 15:2004 



A.nm 


X 10 (2) 


yioU) 


Z10W 


x 10 (A) 


yio(>t) 


710 


0,004 553 


0,001 768 


0,000 000 


0,720 23 


0,279 77 


715 


0,003 145 


0,001 222 


0,000 000 


0,720 09 


0,279 91 


720 


0,002 175 


0,000 846 


0,000 000 


0,719 91 


0,280 09 


725 


0,001 506 


0,000 586 


0,000 000 


0,719 69 


0,280 31 


730 


0,001 045 


0,000 407 


0,000 000 


0,719 45 


0,280 55 


735 


0,000 727 


0,000 284 


0,000 000 


0,719 19 


0,280 81 


740 


0,000 508 


0,000 199 


0,000 000 


0,718 91 


0,281 09 


745 


0,000 356 


0,000 140 


0,000 000 


0,718 61 


0,281 39 


750 


0,000 251 


0,000 098 


0,000 000 


0,718 29 


0,281 71 


755 


0,000 178 


0,000 070 


0,000 000 


0,717 96 


0,282 04 


760 


0,000 126 


0,000 050 


0,000 000 


0,717 61 


0,282 39 


765 


0,000 090 


0,000 036 


0,000 000 


0,717 24 


0,282 76 


770 


0,000 065 


0,000 025 


0,000 000 


0,716 86 


0,283 14 


775 


0,000 046 


0,000 018 


0,000 000 


0,716 46 


0,283 54 


780 


0,000 033 


0,000 013 


0,000 000 


0,716 06 


0,283 94 



Summation at 5 nm intervals: 

]Tx 10 (A) = 23,329 353 ^]y 10 (A)- 23,332036 ]Tz 10 (2) -23,334153 !! 



11.6 Table T.6. Relative spectral power distributions of illuminants representing 
typical fluorescent lamps, for wavelengths 2=380nm to 780 nm at 5 nm 
intervals 

Table 7.6.1 Fluorescent lamps FL1-12, already published In CIE 15.2 as F1-F12 xvm . 

FL1-6: standard; FL7-9: broad-band; FL10-12: narrow band fluorescent lamps. 



X, nm 


FL1 


FL2* 


FL3 


FL4 


FL5 


FL6 


FL7* 


FL8 


FL9 


FL10 


FL11* 


FL12 


380 


1,87 


1,18 


0,82 


0,57 


1,87 


1,05 


2,56 


1.21 


0,90 


1,11 


0,91 


0,96 


385 


2,36 


1,48 


1,02 


0.70 


2,35 


1,31 


3,18 


1,50 


1,12 


0,80 


0,63 


0,64 


390 


2,94 


1,84 


1,26 


0,87 


2,92 


1,63 


3,84 


1,81 


1,36 


0,62 


0,46 


0,40 


395 


3,47 


2,15 


1,44 


0,98 


3,45 


1,90 


4,53 


2,13 


1,60 


0,57 


0,37 


0,33 


400 


5,17 


3,44 


2,57 


2,01 


5,10 


3,11 


6,15 


3,17 


2,59 


1,48 


1,29 


1,19 


405 


19,49 


15,69 


14,36 


13,75 


18,91 


14.80 


19.37 


13,08 


12,80 


12,16 


12,68 


12,48 


410 


6,13 


3,85 


2,70 


1,95 


6,00 


3,43 


7,37 


3,83 


3,05 


2,12 


1,59 
1 79 


1,12 
0,94 


415 


6,24 


3,74 


2,45 


1.59 


6,11 


3,30 


7,05 


3,45 


2,56 


2,70 


420 


7,01 


4,19 


2,73 


1,76 


6,85 


3.68 


7,71 


3,86 


2,86 


3,74 


2,46 


1.08 


425 


7,79 


4,62 


3,00 


1,93 


7,58 


4,07 


8,41 


4,42 


3,30 


5,14 


3,33 


1,37 


430 


8,56 


5,06 


3,28 


2,10 


8,31 


4,45 


9,15 


5,09 


3,82 


6,75 


4,49 


1,78 


435 


43,67 


34,98 


31,85 


30,28 


40,76 


32,61 


44,14 


34,10 


32,62 


34,39 


33,94 


29,05 


440 


16,94 


11,81 


9,47 


8,03 


16,06 


10,74 


17,52 


12,42 


10,77 


14,86 


12,13 


7,90 



xvm liiuminants FL2*, FL7* and FL11* should take priority over others when a few typical 
fluorescent lamp illuminants are to be selected. 



40 



CIE 15:2004 



a, nm 


FL1 


FL2* 


FL3 


FL4 


FL5 


FL6 


FL7* FL8 


FL9 


FL10 


FL11* 


FL12 


445 


10,72 


6,27 


4,02 


2,55 


10,32 


5,48 


11,35 


7,68 


5,84 


10,40 


6,95 


2,65 


450 


11,35 


6,63 


4,25 


2,70 


10,91 


5,78 


12,00 


8,60 


6,57 


10,76 


7,19 


2,71 


455 


11,89 


6,93 


4,44 


2,82 


11,40 


6,03 


12,58 


9,46 


7,25 


10,67 


7,12 


2,65 


460 


12,37 


7,19 


4,59 


2,91 


11,83 


6 ; 25 


13,08 


10,24 


7,86 


10,11 


6,72 


2,49 
2,33 


465 


12,75 


7.40 


4,72 


2,99 


12,17 


6,41 


13,45 


10,84 


8,35 


9,27 


6,13 


470 


13,00 


7,54 


4.80 3,04 


12,40 


6,52 


13,71 


11,33 


8,75 


8,29 


5,46 | 2,10 


475 


13,15 


7,62 


4,86 i 3,08 


12,54 


6,58 


13,88 


11,71 


9,06 


7,29 


4,79 


1,91 


480 


13,23 


7,65 


4,87 


3,09 


12,58 


6,59 


13,95 


11,98 


9,31 


7,91 


5,66 


3,01 


485 


13,17 


7,62 


4,85 


3,09 


12,52 


6,56 


13,93 


12,17 


9,48 


16,64 


14,29 


10,83 


490 


13.13 


7,62 


4,88 


3,14 


12,47 


6.56 


13,82 


12,28 


9,61 


16,73 


14,96 


11,88 


495 


12,85 


7,45 


4,77 


3,06 


12,20 


6,42 


13,64 


12,32 


9,68 


10,44 


8,97 


6,88 


500 


12,52 


7,28 


4,67 


3,00 


11,89 


6,28 


13,43 


12,35 


9,74 


5,94 


4,72 


3,43 


505 


12,20 


7,15 


4,62 


2,98 


11,61 


6,20 


13,25 


12,44 


9,88 | 3,34 


2,33 


1,49 


510 


11,83 


7,05 


4,62 


3,01 


11,33 


6,19 


13,08 


12,55 


10,04 


2,35 


1,47 


0,92 


515 


11,50 


7,04 


4,73 


3,14 


11,10 


6,30 


12,93 


12,68 


10,26 


1,88 


1.10 


0,71 


520 


11,22 


7,16 


4,99 


3,41 


10,96 


6,60 


12,78 


12,77 


10,48 | 1,59 


0,89 


0,60 


525 

530 


11,05 


7,47 


5,48 


3,90 


10,97 


7.12 


12,60 


12,72 


10,63 | 1,47 


0,83 


0,63 


11,03 


8,04 


6,25 


4,69 


11.16 


7,94 


12,44 


12,60 


10,78 


1,80 


1,18 


1,10 


535 


11.18 


8,88 


7,34 


5,81 


11,54 


9,07 


12,33 


12,43 


10,96 


5,71 


4,90 


4,56 


540 


11,53 


10,01 


8,78 


7,32 


12,12 


10,49 


12,26 


12,22 


11,18 


40,98 


39,59 


34,40 


545 


27,74 


24,88 


23,82 


22,59 


27,78 


25,22 


29,52 


28,96 


27,71 


73,69 


72,84 


65,40 


550 


17,05 


16,64 


16,14 


15.11 


17,73 


17,46 


17,05 


16,51 


16.29 


33,61 


32,61 


29,48 


555 


13,55 


14,59 


14,59 


13,88 


14,47 


15,63 


12,44 


11.79 


12,28 


8,24 


7,52 


7,16 


560 


14,33 


16,16 


16,63 


16,33 


15,20 


17,22 


12.58 


11,76 


12,74 


3,38 


2,83 


3.08 


565 


15,01 


17,56 


18,49 


18,68 


15,77 


18,53 


12,72 


11,77 


13,21 


2,47 


1,96 


2,47 


570 


15,52 


18,62 


19,95 


20,64 


16,10 


19,43 


12,83 


11,84 


13,65 


2,14 


1,67 


2,27 


575 


18,29 


21,47 


23,11 


24,28 


18,54 


21,97 


15,46 


14,61 


16,57 


4,86 


4,43 


5,09 


580 


19,55 


22,79 


24,69 


26,26 


19,50 


23,01 


16,75 


16,11 


18,14 


11,45 


11,28 


11,96 


585 


15,48 


19,29 


21,41 


23,28 


15,39 


19,41 


12,83 


12,34 


14,55 


14,79 


14,76 


15,32 


590 


14,91 


18,66 


20,85 


22,94 


14,64 


18,56 


12,67 


12,53 


14,65 


12,16 


12,73 


14,27 


595 


14,15 


17,73 


19,93 


22.14 


13,72 


17,42 


12,45 


12,72 


14,66 


8,97 


9,74 


11,86 


600 


13,22 


16,54 


18,67 


20 91 


12,69 


16,09 


12,19 


12,92 


14,61 


6.52 


7,33 


9,28 


605 


12,19 


15,21 


17,22 


19,43 


11,57 


14,64 


11,89 


13,12 


14,50 


8,31 


9,72 


12,31 


610 


11,12 


13,80 


15,65 


17,74 


10,45 


13,15 


11,60 


13,34 


14,39 


44,12 


55,27 


68,53 


615 


10,03 


12,36 


14,04 


16,00 


9,35 


11,68 


11,35 


13,61 


14,40 


34,55 


42,58 


53,02 


620 


! 8,95 


10,95 


12,45 


14,42 


8,29 


10,25 


11,12 


13,87 


14,47 


12,09 


13,18 


14,67 


625 


I 7,96 


9,65 


10,95 


12,56 


7,32 


8,95 


10,95 


14,07 


14,62 


12,15 


13,16 


14,38 


630 
635 
640 
645 
650 


7,02 


8,40 


9,51 


10,93 


6,41 


7,74 


10,76 


14,20 


14,72 


10,52 


12,26 


14,71 


6,20 


7,32 


8,27 


9,52 


5,63 


6,69 


10,42 


14,16 


14,55 


4,43 


5,11 


6.46 


5 42 


6,31 


7,11 


8,18 


4,90 


5,71 


10,11 


14,13 


14,40 


1,95 


2,07 


2,57 


4,73 


5 43 


6,09 


7,01 


4,26 


4,87 


10,04 


14,34 


14,58 


2,19 


2,34 


2,75 


4,15 


4,68 


5,22 


6,00 


3,72 


4,16 


10,02 


14,50 


14,88 


3,19 


3,58 


4.18 



41 



CIE 15:2004 



X, nm 


FL1 


FL2* 


FL3 


FL4 


FL5 


FL6 


FL7* 


FL8 


FL9 


FL10 


FL11* 


FL12 


655 


3,64 


4,02 


4,45 


5,11 


3,25 


3,55 


10,11 


14,46 


15,51 


2,77 


3,01 


3,44 


660 


3,20 


3,45 


3,80 


4,36 


2.83 


3,02 


9,87 


14,00 


15,47 


2,29 


2,48 


2,81 


665 


2.81 


2,96 


3,23 


3,69 


2,49 


2,57 


8,65 


12,58 


13,20 


2,00 


2,14 


2,42 


670 


2,47 


2,55 


2,75 


3,13 


2,19 


2,20 


7.27 


10,99 


10,57 


152 


1,54 


1,64 


675 


2,18 


2,19 


2,33 


2,64 


1,93 


1,87 


6,44 


9,98 


9,18 


135 


133 


136 


680 


1,93 


1,89 


1,99 


2,24 


1,71 


1,60 


5,83 


9,22 


8,25 


147 


1,46 


1,49 


685 


1,72 


1,64 


1,70 


1,91 


152 


137 


5,41 


8,62 


7,57 


1,79 


1,94 


2,14 


690 


1.67 


1,53 


1.55 


170 


148 


1,29 


5,04 


8,07 


7,03 


174 


2,00 


2,34 


695 


1,43 


1,27 


1,27 


1,39 


1,26 


1,05 


4,57 


7,39 


6,35 


1,02 


1,20 


142 


700 


1,29 


1 10 


1,09 


1,18 


1,13 


0,91 


4,12 


6,71 


5,72 


114 


135 


1,61 


705 


1,19 


0,99 


0,96 


1,03 


1,05 


0,81 


3,77 


6,16 


5,25 


3,32 


4.10 


5,04 


710 


1,08 


0,88 


0,83 


0,88 


0,96 


0,71 


3,46 


5,63 


4,80 


4,49 


5,58 


6,98 


715 


0,96 


0,76 


0.71 


0,74 


0,85 


0,61 


3,08 


5,03 


4,29 


2,05 


2.51 


3,19 


720 


0,88 


0,68 


0,62 


0.64 


0,78 


0,54 


2,73 


4,46 


3,80 


0,49 


0,57 


0,71 


725 


0,81 


0,61 


0.54 


0,54 


0,72 


0,48 


2.47 


4,02 


3,43 


0,24 


0,27 


0,30 


730 


0.77 


0,56 


0,49 


0,49 


0,68 


0,44 


2,25 


3,66 


3,12 


0,21 


0,23 


0,26 


735 


0,75 


0,54 


0,46 


0,46 


0,67 


0,43 


2,06 


3,36 


2,86 


0,21 


0,21 


0,23 


740 


0,73 


0,51 


0,43 


0,42 


0,65 


0,40 


1,90 


3,09 


2,64 


0.24 


0,24 


0,28 


745 


0,68 


0.47 


0,39 


0,37 


0,61 


0,37 


175 


2,85 


2,43 


0,24 


0,24 


0,28 


750 


0,69 


0,47 


0,39 


0,37 


0,62 


0,38 


1,62 


2,65 


2,26 


0,21 


0,20 


0,21 


755 


0.64 


0,43 


0,35 


0,33 


0,59 


0,35 


1,54 
1,45 


2,51 


2,14 


0,17 


0,24 


0,17 


760 


0,68 


0,46 


0,38 


0,35 


0,62 


0,39 


2,37 


2,02 


0,21 


0,32 


0,21 


765 


0,69 


0,47 


0,39 


0,36 


0,64 


0,41 


1,32 


2,15 


1,83 


0,22 


0,26 


0,19 


770 


0,61 


0,40 


0,33 


0.31 


0,55 


0,33 


117 


1,89 


1,61 


0,17 


0,16 


0,15 


775 


0,52 


0,33 


0,28 


0,26 


0,47 


0,26 


0,99 


1,61 


1,38 


0,12 


0,12 


0,10 


780 


0,43 


0,27 


0,21 


0.19 


0,40 


0,21 


0.81 


132 


1,12 


0,09 


0,09 


0,05 



42 



CI E 15:2004 



Table T.6.2.a. New set of fluorescent lamps. FL3.1-3: Standard halophosphate lamps; 
FL3.4-6: DeLuxe type lamps; FL3.7-8: Three band fluorescent iamps. 



X, nm + 


FL3.1 


FL3.2 


FL3.3 


FL3.4 


FL3.5 


FL3.6 


FL3.7 


FL3.8 


380 


2,39 


5,80 


8,94 


3,46 


4,72 


5,53 


3,79 


4,18 


385 


2,93 


6,99 


11,21 


3,86 


5,82 


6,63 


2,56 


2,93 


390 


3,82 


8,70 


14,08 


4,41 


7,18 


8,07 


1,91 


2,29 


395 


4,23 


9,89 


16,48 


4,51 


8,39 


9,45 


1,42 


1,98 


400 


4,97 


11,59 


19,63 


4,86 


9,96 


11,28 


1,51 


2,44 


405 


86,30 


94,53 


116,33 


71,22 


58,86 


61,47 


73,64 


70,70 


410 


11,65 


20,80 


32,07 


8,72 


15,78 


17,80 


7,37 


10,19 


415 


7,09 


16,52 


29,72 


5,36 


15,10 


17,47 


4,69 


9,79 


420 


7,84 


18,30 


33,39 


5,61 


17,30 


20,12 


5,33 


13,21 


425 


8,59 


20,33 


36,94 


5,91 


19,66 


23,05 


6,75 


17,79 


430 


9,44 


22,00 


40,33 


6,42 


22,43 


26,37 


8,51 


22,98 


435 


196,54 


231,90 


262,66 


192,77 


176,00 


186,01 


181,81 


191,43 


440 


10,94 


25,81 


46,87 


7,77 


28,67 


33,94 


11,71 


31,76 


445 


11,38 


27,63 


49,79 


8,37 


31,92 


37,98 


11,96 


33,35 


450 


11,89 


29,10 


52,46 


9,22 


35,38 


42,12 


12,18 


33,87 


455 


12,37 


30,61 


54,81 


10,18 


38,73 


46,38 


11,90 


32,89 


460 


12,81 


31,92 


56,81 


11,18 


41,98 


50,30 


11,16 


30,60 


465 


13,15 


33,11 


58,44 


12,28 


44,92 


53,95 


11,22 


28,28 


470 


13,39 


33,83 


59,52 


13,38 


47,49 


56,94 


9,83 


24,81 


475 


13,56 


34,70 


60,12 


14,54 


49,58 


59,48 


8,94 


21,60 


480 


13,59 


35,02 


60,24 


15,74 


51,21 


61,36 


12,08 


23,40 


485 


13,56 


35,22 


59,88 


17,09 


52,36 


62,68 


52,56 


68,99 


490 


14,07 


35,81 


59,88 


19,60 


53,99 


64,34 


55,42 


70,85 


495 


13,39 


35,14 


58,60 


21,05 


53,78 


63,90 


31,69 


42,29 


500 


13,29 


35,14 


57,85 


23,96 


54,04 


63,85 


16,03 


22,67 


505 


13,25 


34,90 


56,29 


27,77 


53,88 


63,24 


6,72 


11,08 


510 


13,53 


34,70 


54,81 


32,68 


53,62 


62,46 


4.59 


7,66 


515 


14,24 


35,02 


53,42 


38,29 


53,25 


61,41 


3,67 


6,07 


520 


15,74 


36,13 


52,70 


43,76 


53,09 


60,47 


3,02 


5,07 


525 


18,26 


37,92 


52,50 


47,72 


52,88 


59,48 


3,21 


4,88 


530 


22,28 


40,62 


53,30 


50,27 


52,99 


58,65 


4,90 


6,26 


535 


27,97 


44,70 


54,89 


51,78 


53,15 


57,93 


19,05 


20,29 


540 


35,70 


49,63 


57,61 


52,68 


53,67 


57,49 


177,64 


204,67 


545 


148.98 


154,16 


182,75 


167,36 


167,93 


175,17 


347,34 


390,25 


550 


56,55 


62,21 


65,27 


55,29 


55,61 


57,27 


116,80 


135,69 


555 


68,68 


68,92 


69,41 


56,94 


56,82 


57,49 


31,87 


34,57 


560 


79,99 


75,83 


73,28 


59,30 


58,39 


57,99 


16,37 


15,71 


565 


91,47 


81,95 


76,56 


62,15 


60,22 


58,76 


14,92 


12,60 


570 


101,32 


86,95 


78,67 


65,26 


62,21 


59,64 


14,12 


11,05 


575 


123,16 


103,54 


95,74 


84,26 


81,45 


78,77 


29,50 


25,05 


580 


129,53 


109,94 


97,22 


89,22 


84,96 


81,26 


61,40 


54,98 


585 


115,05 


91,95 


76,79 


75,79 


68,71 


63,18 


85,05 


82,84 



43 



C!E 15:2004 



X, nm + 


FL3.1 


FL3.2 


FL3.3 


FL3.4 


FL3.5 


FL3.6 


FL3.7 


FL3.8 


590 


113,48 


89,85 


73,36 


79,19 


70,70 


64,29 


64,86 


58,22 


595 


110,08 


87,15 


69,33 


82,80 


73,01 


65,78 


65,01 


53,06 


600 


104,28 


83,26 


64,23 


85,76 


74,69 


66,77 


53,17 


41,44 


605 


97,98 


78,93 


58,92 


88,62 


76,26 


67,77 


34,22 


25,26 


610 


89,60 


73,93 


53,38 


91,12 


77,68 


68,60 


427,27 


329,89 


615 


80,74 


68,84 


47,91 


93,43 


78,67 


69,10 


201,10 


161,29 


620 


71,92 


63,44 


42,61 


96,89 


80,14 


70,15 


58,63 


54,19 


625 


63,50 


58,84 


37,74 


101,45 


81,71 


71,69 


72,01 


66,30 


630 


55,46 


53,84 


33,11 


103,65 


82,08 


71,97 


88,19 


71,43 


635 


47,97 


49,43 


29,04 


100,30 


79,98 


69,81 


20,07 


15,74 


640 


41,39 


45,54 


25,29 


97,89 


78,15 


68,05 


13,10 


10,22 


645 


35,50 


41,53 


22,10 


96,59 


76,52 


66,66 


12,92 


10,68 


650 


30,32 


38,31 


19,31 


106,21 


79,20 


69,70 


24,54 


20,32 


655 


25,79 


34,62 


16,84 


109,97 


79,51 


70,37 


15,94 


14,13 


660 


21,84 


31,80 


14,68 


117,49 


81,08 


72,47 


13,56 


11,72 


665 


18,53 


29,02 


12,89 


96,04 


7076 


62,30 


13,38 


11,75 


670 


15,67 


26,72 


11,37 


80,15 


62,58 


54,45 


8,42 


7,87 


675 


13,22 


24,22 


9,97 


70,42 


56,87 


49,20 


6,57 


6,38 


680 


11,14 


22,19 


8,82 


65,01 


52,83 


45,60 


7,18 


7,23 


685 


9,40 


20,41 


7,86 


60,15 


49,11 


42,40 


9,90 


8,94 


690 


8,65 


19,10 


7,78 


56,04 


46,28 


40,02 


11,47 


9,79 


695 


6,75 


16,79 


6,30 


50,92 


42,24 


36,48 


8,88 


7,26 


700 


5,69 


15,13 


5,67 


46,26 


38,58 


33,28 


3.05 


2,59 


705 


4,87 


13,82 


5,15 


42,60 


35,59 


30,84 


22,04 


17,03 


710 


4,29 


12,63 


4,91 


38,85 


32,76 


23,30 


42,79 


33,69 


715 


3,54 


11,39 


4,31 


35,09 


29,61 


25,65 


14,40 


12,02 


720 


3,03 


10,32 


3,99 


31,73 


26,89 


23,33 


1,88 


1,68 


725 


2,62 


9,21 


3,67 


28,77 


24,53 


21,23 


1,60 


1,50 


730 


2,28 


8,89 


3,43 


25,76 


22,17 


19,29 


1,42 


1,31 


735 


1,94 


7,50 


3,19 


23,16 


20,02 


17,41 


1,05 


1,01 


740 


1,70 


6,71 


2,95 


21,30 


18,45 


16,31 


1,23 


1,16 


745 


1,50 


6,11 


2,75 


18,55 


16,09 


14,21 


1,76 


1,59 


750 


1,36 


5,40 


2,63 


17,74 


15,62 


14,04 


0,74 


0,79 


755 


1,16 


4,80 


2,43 


14,74 


13,10 


11,55 


0,52 


0,67 


760 


4,91 


8,70 


7,14 


12,93 


11,69 


10,39 


4,10 


4,82 


765 


0,95 


4,01 


2,19 


13,63 


12,42 


11,28 


0,46 


0,61 


770 


1,50 


4,09 


2,71 


10,43 


9,43 


8,51 


0,99 


1,25 


775 


0,89 


3,30 


2,00 


9,67 


8,96 


8,24 


0,43 


0,79 


780 


0,68 


2,82 


1,80 


8,07 


7,39 


7,02 


0,00 


0,58 



+ This table gives the representative data of these lamps only in the 380 nm to 780 nm 
region for colorimetric purposes, though many fluorescent lamps emit power outside this 
spectral region, especially in the near ultraviolet. Other sources of data must be consulted if 
information is required below 380 nm or above 780 nm. 



44 



CiE 15:2004 



Table T.6.2b. New set of fluorescent lamps, cont FL3.9-11: Three band fluorescent lamps; 
FL3.12-14: Multi-band fluorescent lamps; FL3.15: D65 simulator lamp. 



X, nm + [ FL3.9 


FL3.10 


FL3.11 


FL3.12 


FL3.13 


FL3.14 


FL3.15 


380 


3,77 


0,25 


3,85 


1,62 


2,23 


2,87 


300,00 


385 


2,64 





2,91 


2,06 


2,92 


3,69 


286,00 


390 


2,06 





2,56 


2,71 


3,91 


4,87 


268,00 


395 


1,87 





2,59 


3,11 


4,55 


5,82 


244,00 


400 


2,55 


0,69 


3,63 


3,67 


5,46 


7,17 


304,00 


405 


71,68 


21,24 


74,54 


74,60 


77,40 


72,21 


581,00 


410 


12,05 


2,18 


14,69 


8,88 


11,25 


13,69 


225,00 


415 


13,57 


1,86 


17,22 


4,77 


7,69 


11,12 


155,00 


420 


19,60 


3,1 


24,99 


4,72 


8,29 


12,43 


152,00 


425 


27,33 


5 


34,40 


4,72 


8,98 


13,90 


170,00 


430 


35,39 


7,03 


44,57 


4,94 


10,01 


15,82 


295,00 


435 


211,82 


45,08 


228,08 


150,29 


204,45 


200,99 


1 417,00 


440 


49,02 


16,78 


61,53 


6,08 


13,75 


21,72 


607,00 


445 


51,83 


12,28 


65,31 


7,13 


16,88 


26,33 


343,00 


450 


52,50 


13,31 


66,35 


9,10 


21,73 


32,85 


386,00 


455 


50,73 


13,66 


64,37 


11,76 


27,96 


40,80 


430,00 


460 


46,93 


13,69 


59,81 


14,96 


34,92 


49,23 


469,00 


465 


42,42 


13,13 


54,24 


18,54 


41,96 


57,39 


502,00 


470 


37,16 


12,28 


47,42 


22,48 


48,62 


65,26 


531,00 


475 


31,84 


11,42 


41,10 


26,76 


54,33 


71,99 


552,00 


480 


31,94 


11,66 


40,04 


31,66 


59,49 


78,25 


567,00 


485 


77,74 


22,04 


85,54 


40,93 


67,91 


88,85 


572,00 


490 


79,45 


26,17 


86,55 


45,83 


70,01 


91,67 


575,00 


495 


47,93 


18,57 


53,47 


46,00 


66,40 


86,81 


561,00 


500 


26,24 


11,36 


30,91 


45,26 


62,07 


80,42 


548,00 


505 


13,15 


6,83 


17,41 


43,16 


56,95 


73,82 


527,00 


510 


8,80 


5,58 


12,56 


41,63 


52,70 


69,12 


507,00 


515 


6,70 


4,88 


10,10 


39,75 


48,54 


63,69 


482,00 


520 


5,38 


4,31 


8,48 


37,83 


44,80 


58,44 


461,00 


525 


4,93 


3,76 


7,74 


36,16 


41,75 


53,57 


438,00 


530 


6,06 


3,61 


8,58 


35,25 


39,77 


49,66 


418,00 


535 


19,76 


5,62 


21,39 


37,04 


40,50 


48,44 


404,00 


540 


215,94 


38,59 


220,12 


59,86 


59,27 


72,56 


429,00 


545 


412,13 


100 


417,35 


183,53 


184,09 


200,42 


1016,00 


550 


142,39 


36,54 


146,13 


59,03 


59,06 


65,00 


581,00 


555 


34,74 


10,57 


36,67 


47,93 


49,95 


47,49 


370,00 


560 


14,76 


2,98 


16,51 


48,67 


50,90 


44,14 


368,00 


565 


10,99 


2,05 


12,56 


52,69 


54,51 


44,71 


371,00 


570 


9,25 


1,84 


10,81 


57,24 


58,33 


46,01 


377,00 


575 


23,50 


6,09 


25,31 


77,75 


77,49 


63,52 


490,00 


580 


53,05 


17,27 


53,31 


87,81 


85,78 


71,73 


525,00 


585 


81,90 


21,77 


80,75 


80,55 


76,20 


63,52 


402,00 



45 



CIE 15:2004 



X, nm + 


FL3.9 


FL3.10 


FL3.11 


FL3.12 


FL3.13 


FL3.14 


FL3.15 


590 


54,92 


18,72 


53,56 


84,83 


78,73 


64,13 


404,00 


595 


47,80 


10,15 


44,02 


86,84 


78,95 


63,74 


412,00 


600 


36 } 65 


7,26 


33,05 


91,44 


81,48 


66,82 


418,00 


605 


21,82 


5,17 


20,26 


96,51 


84,57 


70,65 


425,00 


610 


285,69 


56,66 


233,61 


105,25 


87,75 


79,29 


428,00 


615 


139,94 


49,39 


118,20 


106,74 


89,56 


80,77 


432,00 


620 


53,37 


18.57 


51,66 


108,53 


91,36 


83,59 


433,00 


625 


64,30 


14,21 


61,27 


106,92 


89,00 


82,59 


431,00 


630 


64,04 


14,01 


55,15 


101,54 


83,67 


77,60 


427,00 


635 


13,79 


5,99 


12,95 


95,20 


78,26 


72,47 


420,00 


640 


9,06 


2,68 


8,93 


89,34 


73,19 


68,34 


410,00 


645 


9,83 


3,14 


9,77 


82,95 


67,61 


63,82 


399,00 


650 


18,60 


6.25 


17,12 


75,78 


61,42 


58,57 


385,00 


655 


13,38 


5,78 


13,01 


68,65 


55,49 


53,18 


370,00 


660 


10,99 


6,75 


10,45 


61,70 


49,78 


47,97 


352,00 


665 


10,77 


5,16 


10,33 


55,23 


44,46 


43,14 


336,00 


670 


7,57 


3,03 


7,70 


48,58 


39,13 


38,19 


317,00 


675 


6,19 


1,57 


6,34 


42,90 


34,45 


33,85 


298,00 


680 


7,09 


1,72 


7,35 


37,74 


30,28 


29,94 


277,00 


685 


8,54 


1,54 


8,22 


32,93 


26,37 


26,24 


260,00 


690 


8,77 


1,71 


7,93 


29,65 


23,88 


23,90 


242,00 


695 


6,41 


1,1 


5,70 


25,19 


20,10 


20,33 


223,00 


700 


2,26 


0,28 


2,23 


21,69 


17,40 


17,42 


202,00 


705 


15,02 


3,65 


12,43 


19,28 


15,29 


15,64 


187,00 


710 


29,39 


7,54 


24,24 


17,36 


13,62 


14,34 


167,00 


715 


10,22 


2,34 


8,74 


14,74 


11,68 


12,21 


152,00 


720 


1,42 


0,05 


1,39 


12,86 


10,31 


10,65 


136,00 


725 


1,23 


0,04 


1,23 


11,28 


9,11 


9,43 


125,00 


730 


1,10 


0,04 


1,10 


9,97 


8,03 


8,34 


113,00 


735 


0,84 


0,03 


0,84 


8,88 


7,13 


7,52 


103,00 


740 


0,97 


0,03 


0,94 


7,78 


6,31 


6,73 


93,00 


745 


1,35 


0,02 


1,23 


7,04 


5,67 


6,08 


84,00 


750 


0,65 


0,02 


0,68 


6,30 


5,11 


5,52 


75,00 


755 


0,13 


0,01 


0,52 


5,55 


4,55 


5,00 


66,00 


760 


4,22 


0,01 


4,60 


10,15 


9,06 


9,47 


58,00 


765 


0,10 





0,45 


4,50 


3,74 


4,08 


51,00 


770 


0,68 





1,04 


4,81 


4,04 


4,43 


46,00 


775 


0,16 





0,45 


3,72 


3,14 


3,39 


41,00 


780 


0,00 





0,00 


3,28 


2,75 


3,17 


37,00 



+ This table gives the representative data of these lamps only in the 380 nm to 780 nm 
region for coiorimetric purposes, though many fluorescent lamps emit power outside this 
spectral region, especially in the near ultraviolet. Other sources of data must be consulted if 
information is required below 380 nm or above 780 nm. 



46 



CI E 15:2004 



11.7 Table T.7. High pressure discharge lamps. HP1: Standard high pressure sodium 
lamp; HP2: Colour enhanced high pressure sodium Samp; HP3-5: Three types of 
high pressure metal halide lamps 



X, nm + 


HP1 


HP2 




HP3 


HP4 


HP5 


380 


1,90 


2,64 




3,15 


9,80 


0,34 


385 


2,20 


2,77 




7,49 


13,30 


7,11 


390 


2,50 


3,42 




10,87 


19,97 


11,49 


395 


2,70 


3,68 




12,57 


25,81 


14,97 


400 


3,10 


4,33 




12,97 


24,69 


14,95 


405 


4,30 


5,50 




21,29 


47,66 


29,14 


410 


3,80 


5,94 




26,29 


54,44 


38,08 


415 


4,20 


7,20 




30,18 


63,82 


51,56 


420 


4,80 


9,02 




43,06 


85,52 


62,56 


425 


5,19 


10,27 




29,58 


60,54 


55,61 


430 


5,89 


12,48 




23,18 


38,37 


41,98 


435 


7,39 


16,82 




35,28 


88,20 


50,02 


440 


7,89 


16,04 




26,29 


44,94 


42,14 


445 


5,69 


15,26 




24,29 


35,64 


39,04 


450 


12,89 


22,58 




22,91 


30,75 


40,52 


455 


6,69 


20,07 




26,20 


33,77 


45,29 


460 


4,30 


15,13 




29,31 


40,81 


51,01 


465 


20,78 


25,27 




25,30 


33,77 


49,18 


470 


12,99 


28,04 




28,14 


35,28 


49,05 


475 


6,69 


15,99 




24,05 


32,55 


46,12 


480 


1,40 


10,40 




21,82 


29,44 


45,73 


485 


1,50 


11,10 




20,51 


26,16 


39,46 


490 


3,20 


13,44 




23,05 


29,96 


44,39 


495 


18,18 


22,62 




26,98 


32,83 


46,14 


500 


56,24 


49,71 




30,96 


33,58 


49,54 


505 


2,90 


17,21 




30,72 


41,16 


59,76 


510 


2,10 


17,12 




27,13 


32,93 


48,47 


515 


13,39 


27,26 




29,55 


32,13 


48,38 


520 


2,10 


20,02 




34,22 


34,45 


48,70 


525 


2,00 


21,54 




29,98 


30,12 


44,25 


530 


2,20 


23,36 




41,21 


41,13 


54,42 


535 


2,30 


25,66 




173,14 


187,10 


128,93 


540 


2,60 


29,69 




141,37 


101,37 


81,26 


545 


5,10 


43,12 




64,98 


123,96 


67,36 


550 


11,39 


98,30 




33,83 


42,47 


48,48 


555 


15,48 


125,60 




34,26 


34,73 


51,41 


560 


20,78 


134,57 




33,32 


31,82 


48,88 


565 


55,64 


149,70 




52,80 


54,67 


68,52 


570 


254,03 


166,12 




74,29 


57,45 


80,85 


575 


56,14 


98,77 




47,97 


70,43 


65,96 


580 


111,78 


30,47 




49,20 


69,50 


59,43 



47 



CIE 15:2004 



A, nm + 


HP1 


HP2 




HP3 


HP4 


HP5 


585 


297,98 


1,17 




96,07 


49,37 


67,57 


590 


142,55 


0,39 




85,41 


183,35 


128,34 


595 


334,84 


1,65 




175,18 


162,15 


131,85 


600 


189,40 


21,41 




153,73 


109,35 


101,70 


605 


117,78 


76,11 




120,22 


72,38 


77,05 


610 


79,92 


126,16 




98,90 


70,60 


66,27 


615 


108,09 


161,96 




90,22 


58,08 


77,09 


620 


46,85 


160,06 




70,07 


44,13 


60,51 


625 


38,16 


158,19 




66,84 


50,20 


65,23 


630 


32,47 


153,69 




57,61 


40,80 


57,86 


635 


28,37 


147,40 




53,03 


37,91 


56,20 


640 


25,37 


140,60 




49,85 


36,71 


54,32 


645 


22,98 


134,92 




48,16 


38,30 


56,34 


650 


20,38 


127,59 




42,76 


31,24 


45,74 


655 


19,78 


124,65 




50,64 


35,31 


50,79 


660 


17,78 


118,02 




48,42 


45,62 


56,66 


665 


16,78 


113,94 




41,27 


35,82 


51,99 


670 


19,18 


118,10 




43,44 


89,91 


84,31 


675 


17,98 


115,16 




40,48 


36,01 


47,48 


680 


13,69 


102,85 




35,16 


32,57 


47,46 


685 


9,99 


90,54 




34,94 


39,26 


61,78 


690 


8,19 


83,34 




24,68 


23,27 


34,51 


695 


7,59 


79,44 




24,70 


25,30 


38,74 


700 


6,99 


76,97 




21,49 


20,02 


30,98 


705 


6,79 


74,85 




19,49 


17,54 


25,45 


710 


6,49 


73,12 




18,48 


16,25 


22,88 


715 


6,39 


71,51 




17,55 


15,20 


20,82 


720 


6,09 


70,13 




17,36 


15,15 


21,05 


725 


5,99 


69,04 




17,09 


15,22 


20,81 


730 


5,79 


67,48 




16,32 


14,26 


18,69 


735 


5,79 


66,70 




16,07 


12,63 


17,54 


740 


5,79 


66,31 




16,58 


14,75 


19,58 


745 


5,79 


65,14 




15,78 


13,19 


16,42 


750 


6,39 


65,70 




17,66 


17,63 


23,77 


755 


5,99 


64,79 




20,46 


23,38 


35,39 


760 


5,59 


64,10 




16,59 


16,02 


21,37 


765 


31,97 


83,04 




17,81 


24,46 


34,58 


770 


27,87 


86,25 




16,07 


22,05 


30,21 


775 


5,89 


63,93 




14,83 


16,11 


19,71 


780 


6,69 


64,92 




14,61 


12,91 


15,61 



* The relative spectral power distribution of the HP-illuminants given here can only be used 
over the spectral range from 380 nm to 780 nm. Although many high pressure gas discharge 
lamps emit power outside this spectral range, especially in the near ultraviolet, other sources 
of data must be consulted if information is required below 380 nm or above 780 nm. 



48 



CiE 15:2004 

1 1 .8 Table T.8. Colorimetric data for the fluorescent lamp illuminants of Table T.6 

Table T. 8.1. Illuminants as published in Table T.6. 1. 



Lamp 


Chromaticity coordinates 
x y 


Correlated colour 

temperature, (T cp ) 

(kelvlns) 


General colour 
rendering index, R a 


FL1 


0,3131 


0,3371 


6430 


76 


FL2 


0,3721 


0,3751 


4230 


64 


FL3 


0,4091 


0,3941 


3450 


57 


FL4 


0,4402 


0,4031 


2940 


51 


FL5 


0,3138 


0,3452 


6350 


72 


FL6 


0,3779 


0,3882 


4150 


59 


FL7 


0,3129 


0,3292 


6500 


90 


FL8 


0,3458 


0,3586 


5000 


95 


FL9 


0,3741 


0,3727 


4150 


90 


FL 10 


0,3458 


0,3588 


5000 


81 


FL11 


0,3805 


0,3769 


4000 


83 


FL12 


0,4370 


0,4042 


3000 


83 



Table T.8.2. Illuminants as published in Table T.6. 2. 





FL3.1 


FL3.2 


FL3.3 


FL3.4 


FL3.5 


FL3.6 


FL3.7 


x~ 


0,4407 


0,3808 


0,3153 


; 4429 


0,3749 


0,3488 


0,4384 


y= 


0,4033 


0,3734 


0,3439 


0,4043 


0,3672 


0,36 


0,4045 


7"cp= 


2932 K 


3965 K 


6280 K 


2904 K 


4086 K 


4894 K 


2979 K 


Special Rendering Indexes: 


No. 1 = 


42 


65 


64 


91 


97 


97 


97 


No. 2 = 


69 


80 


80 


89 


97 


97 


94 


No. 3 = 


89 


89 


89 


79 


92 


93 


54 


No. 4 = 


39 


66 


69 


88 


94 


97 


88 


No. 5 = 


41 


66 


69 


88 


97 


97 


86 


No. 6 = 


52 


71 


74 


82 


95 


95 


81 


No. 7 = 


66 


79 


81 


88 


94 


96 


87 


No. 8 = 


13 


48 


49 


89 


94 


96 


64 


No. 9 = 


-109 


-37 


-63 


76 


88 


93 


-9 


No. 10 = 


29 


51 


52 


69 


90 


90 


51 


No. 11 = 


19 


56 


62 


88 


95 


97 


76 


No. 12 = 


21 


59 


68 


63 


90 


92 


50 


No. 13 = 


47 


68 


68 


91 


97 


98 


98 


No. 14 = 


93 


94 


93 


87 


95 


95 


69 


General Colour Rendering index 


*a = 


51 


70 


72 


87 


95 


96 


82 



49 



CIE 15:2004 



Table T.8.2 cont. Illuminants as published in Tabie T.6.2. 





FL3.8 


FL3.9 


FL3.10 


FL3.11 


FL3.12 


FL3.13 


FL3.14 


FL3.15 


X- 


0,382 


0,3499 


0,3455 


0,3245 


0,4377 


0,383 


0,3447 


0,3127 


y= 


0,3832 


0,3591 


0,356 


0,3434 


0,4037 


0,3724 


0,3609 


0,3288 


7"c P = 


4006 K 


4853 K 


5000 K 


5854 K 


2984 K 


3896 K 


5045 K 


6509 K 


Special Rendering Indices 


No. 1 = 


94 


94 


99 


90 


95 


98 


93 


99 


No. 2 = 


89 


89 


97 


86 


98 


97 


94 


99 


No. 3 = 


50 


48 


63 


49 


92 


98 


97 


96 


No. 4 = 


85 


84 


92 


82 


95 


97 


94 


98 


No. 5 = 


83 


84 


92 


81 


94 


99 


94 


99 


No. 6 = 


73 


72 


85 


70 


97 


97 


93 


100 


No. 7 = 


86 


85 


92 


85 


93 


94 


97 


98 


No. 8 = 


72 


78 


86 


79 


83 


88 


97 


98 


No. 9 = 


5 


22 


46 


24 


58 


71 


93 


96 


No. 10 = 


40 


38 


62 


34 


88 


99 


91 


99 


No. 1 1 = 


68 


68 


78 


64 


93 


94 


95 


100 


No. 12 = 


48 


51 


72 


50 


85 


89 


85 


95 


No. 13 = 


95 


95 


97 


90 


97 


99 


92 


98 


No. 14 = 


67 


66 


75 


67 


94 


98 


97 


98 


General Colour Rendering Index 


R* = 


79 


79 


88 


78 


93 


96 


95 


98 



11.9 Table T.9. Colorimetric data for the high pressure illuminants of Table T.7 





HP1 


HP2 




HP3 


HP4 


HP5 


x= 


0,533 


0,4778 




0,4302 


0,3812 


0,3776 


y= 


0,415 


0,4158 




0,4075 


0,3797 


0,3713 


^ 


1959 K 


2506 K 




3144 K 


4002 K 


4039 K 


Special Rendering Indices 


No. 1 = 


-3 


98 




87 


75 


87 


No. 2 = 


61 


89 




92 


85 


94 


No. 3 = 


40 


73 




87 


84 


97 


No. 4 = 


-27 


89 




89 


78 


89 


No. 5 = 


-4 


88 




85 


75 


89 


No. 6 = 


52 


71 




90 


79 


94 


No. 7 = 


21 


81 




82 


77 


85 


No. 8 = 


-75 


72 




50 


42 


64 


No. 9 = 


-260 


52 




-29 


-60 


10 


No. 10 = 


43 


66 




71 


56 


85 


No. 11 = 


-52 


66 




89 


77 


90 


No. 12 = 


27 


55 




72 


64 


90 


No. 13 = 


7 


90 




90 


79 


90 


No. 14 = 


61 


82 




91 


91 


98 


General Colour Rendering Index 


Ra = 


8 


83 




83 


74 


87 



50 



CI E 15:2004 



11.10 Table T.10. Values of the first deviation function used in the calculation of the 
observer metamerism index 



X, nm 


Ax(i) 


Ay(A) 


Az(A) 


380 


-0,0001 


0,0000 


-0,0002 


385 


-0,0003 


0,0000 


-0,0010 


390 


-0,0009 


-0,0001 


-0,0036 


395 


-0,0026 


-0,0004 


-0,0110 


400 


-0,0069 


-0,0009 


-0,0294 


405 


-0,0134 


-0,0015 


-0,0558 


410 


-0,0197 


-0,0019 


-0,0820 


415 


-0,0248 


-0,0022 


-0,1030 


420 


-0,0276 


-0,0021 


-0,1140 


425 


-0,0263 


-0,0017 


-0,1079 


430 


-0,0216 


-0,0009 


-0,0872 


435 


-0,0122 


0,0005 


-0,0455 


440 


-0,0021 


0,0015 


^0,0027 


445 


0,0036 


0,0008 


0,0171 


450 


0,0092 


-0,0003 


0,0342 


455 


0,0186 


-0,0005 


0,0703 


460 


0,0263 


-0,0011 


0,0976 


465 


0,0256 


-0,0036 


0,0859 


470 


0,0225 


-0,0060 


0,0641 


475 


0,0214 


-0,0065 


0,0547 


480 


0,0205 


-0,0060 


0,0475 


485 


0,0197 


-0,0045 


0,0397 


490 


0,0187 


-0,0031 


0,0319 


495 


0,0167 


-0,0037 


0,0228 


500 


0,0146 


-0,0047 


0,0150 


505 


0,0133 


-0,0059 


0,0117 


510 


0,0118 


-0,0060 


0,0096 


515 


0,0094 


-0,0025 


0,0062 


520 


0,0061 


0,0010 


0,0029 


525 


0,0017 


0,0005 


0,0005 


530 


-0,0033 


-0,001 1 


-0,0012 


535 


-0,0085 


-0,0020 


-0, 0020 


540 


-0,0139 


-0,0028 


-0,0022 


545 


-0,0194 


-0,0039 


-0,0024 


550 


-0,0247 


-0,0044 


-0,0024 


555 


-0,0286 


-0,0027 


-0,0021 


560 


-0,0334 


-0,0022 


-0,0017 


565 


-0,0426 


-0,0073 


-0,0015 


570 


-0,0517 


-0,0127 


-0,0014 


575 


-0,0566 


-0,0129 


-0,0013 


580 


-0,0600 


-0,0126 


-0,0013 



/L, nm 


Ax(A) 


Ay(Z) 


Az{Z) 


585 


-0,0637 


-0,0162 


-0,001 1 


590 


-0,0656 


-0,0196 


-0,0009 


595 


-0,0638 


-0,0199 


-0,0008 


600 


-0,0595 


-0,0187 


-0,0006 


605 


-0,0530 


-0,0170 


-0,0005 


610 


-0,0448 


-0,0145 


-0,0004 


615 


-0,0346 


-0,0112 


0,0000 


620 


-0,0242 


-0,0077 


0,0002 


625 


-0,0155 


-0,0048 


0.0000 


630 


-0,0085 


-0,0025 


-0,0002 


635 


-0,0044 


-0,0012 


-0,0002 


640 


-0,0019 


-0,0006 


0,0000 


645 


-0,0001 


0,0000 


0,0000 


650 


0,0010 


0,0003 


0,0000 


655 


0,0016 


0,0005 


0,0000 


660 


0,0019 


0,0006 


0,0000 


665 


0,0019 


0,0006 


0,0000 


670 


0,0017 


0,0006 


0,0000 


675 


0,0013 


0,0005 


0,0000 


680 


0,0009 


0,0003 


0,0000 


685 


0,0006 


0,0002 


0,0000 


690 


0,0004 


0,0001 


0,0000 


695 


0,0003 


0,0001 


0,0000 


700 


0,0002 


0,0001 


0,0000 


705 


0,0001 


0,0000 


0,0000 


710 


0,0001 


0,0000 


0,0000 


715 


0,0001 


0,0000 


0,0000 


720 


0,0000 


0,0000 


0,0000 


725 


0,0000 


0,0000 


0,0000 


730 


0,0000 


0,0000 


0,0000 


735 


0,0000 


0,0000 


0,0000 


740 


0,0000 


0,0000 


0,0000 


745 


0,0000 


0,0000 


0,0000 


750 


0,0000 


0,0000 


0,0000 


755 


0,0000 


0,0000 


0,0000 


760 


0,0000 


0,0000 


0,0000 


765 


0,0000 


0,0000 


0,0000 


770 


0,0000 


0,0000 


0,0000 


775 


0,0000 


0,0000 


0,0000 


780 


0,0000 


0,0000 


0,0000 



51 



CIE 15:2004 

APPENDIX A. OLD RECOMMENDATIONS, NOW OBSOLETE, AS WELL AS 
REFERENCES TO NON-CIE COLOUR DIFFERENCE FORMULAE 

Appendix A.1. llluminant B and Source B 

llluminant B 

This illuminant was intended to represent direct sunlight with a correlated colour temperature 
of approximately 4900 K. 

Source B 

llluminant B was realized by source A, combined with a filter consisting of a layer, one 
centimetre thick, of each of two solutions B^ and B 2 , contained in a double cell made of 
colourless optical glass. The solutions were made up as follows: 

Solution B1: 

Copper Sulphate (CuS0 4 ■ 5H 2 0) 

Mannite [C 6 H 8 (OH) 6 ] 

Pyridine (C 5 H 5 N) 

Distilled water to make 
Solution B2: 

Cobalt Ammonium Sulphate [CoS0 4 ) (NH 4 ) 2 S0 4 - 6H 2 0)] 

Copper Sulphate (CuS0 4 .- 5H 2 0) 

Sulphuric Acid (density 1,835 g*ml" 1 ) 

Distilled water to make 



Appendix A.2. llluminant C and Source C 

llluminant C 

Representing average daylight with a correlated colour temperature of about 6800 K. The 
spectral power distribution of llluminant C is reproduced in Table T.1. 

Note: In Table T.1 the values for 775 nm and 780 nm have been added by extrapolation. 

Source C 

llluminant C is to be realized by source A, combined with a filter consisting of a layer, one 
centimetre thick, of each of two solutions C-, and C 2 , contained in a double cell made of 
colourless optical glass. The solutions are to be made up as follows: 

Solution C1: 

Copper Sulphate (CuS0 4 • 5H 2 0) 
Mannite C 6 H 8 (OH) 6 
Pyridine (C 5 H 5 N) 
Distilled water to make 
Solution C2: 

Cobalt Ammonium Sulphate [CoS0 4 . (NH 4 ) 2 S0 4 . 6H 2 0] 30,58 
Copper Sulphate (CuS0 4 . 5H 2 0) 
Sulphuric Acid (density 1 ,835 g-ml" 1 ) 
Distilled water to make 



2,452 


g 


2,452 


g 


30,0 


ml 


1000,0 


ml 


21,71 


g 


16,11 


g 


10,0 


ml 


1000,0 


ml 



3,412 


g 


3,412 


g 


30,0 


ml 


1000,0 


mi 


D] 30,58 


g 


22,52 


g 


10,0 


ml 


1000,0 


ml 



52 



CI E 15:2004 



Appendix A.3. CiE 1964 uniform colour space and colour difference formula 

u, v uniform chromaticity scale (CIE 1960 UCS) diagram 

This approximately uniform chromaticity diagram was produced by plotting 
u = 4X/(X+ 15Y+ 3Z) as abscissa and v = 6YI(X+ 15/+ 3Z) as ordinate; wand vare related 
to u' and \/ of the CIE 1976 UCS diagram by the equations u = u' and v= 2v73. 

7964 uniform space and colour difference formula 

This approximately uniform colour space was produced by plotting along three orthogonal 
axes 

W = 25Y 1/3 -17 

U* = \ZW {u - u n ) 

\/* = 13W*(v-v n ) 

The associated colour difference formula was: 

A£ = [((/*! - U* 2 ) 2 + (\T 1 - V* 2 f + (l/L^ - IV* 2 ) 2 ] 1/2 

The coordinates in this system bear the following approximate relationships to the 
coordinates of the CiELUV space: 

U* = u* 

V* = 2/3 v* 

Appendix A.4. CIE 1994 colour difference formula (CIE94) 

Based on the work documented in CIE 101-1993 (CIE, 1993), where experiments are 
described that pointed out that a number of external parameters of a visual task affect the 
correlation of visual magnitude judgements of colour differences with their colorimetric 
measures, CIE started investigations with carefully selected data sets and reported a new 
colour-difference formula that introduced weighting factors to the lightness, chroma and hue 
differences, AL*, AC* ab and AH* ab , of the CIELAB - formula. The resulting recommendation 
was as follows (CIE, 1995): 



AF* - 

ACT 94 ~ 



\2 

AL* 



f .. +\ 'AC* 1 ( AH' 



k L S L 



_a*L, m 



^C^C J I ^H^H 



The weighting functions, S L , S c , S H adjust the internal non-uniform structure of the 
CIELAB - formula using 

S L =1 

S c = 1 + 0,045 C* ab 

S H = 1 + 0,015 C* ab 

If the standard of a sample pair is not clearly defined, C* ab may be replaced by the 
geometric mean (C* abi1 • C* abi2 ) 1/2 . 

Note 1: The parametric factors, k L , k c , k h are correction terms for variation in experimental 
conditions. Under reference conditions they are all set at 1 . For other choices see 
(CIE, 1993). 

Note 2: An alternative colour difference formula used by some ISO committees, but never 
endorsed by CIE is briefly described in Appendix A. 5. 

Note 3: The CIE 1994 colour difference formula is now obsolete and has been superseded by 
the CIEDE2000 formula. 



53 



C!E 15:2004 



Appendix A.5. CMC(l:c) colour difference formula 

The Colour Measurement Committee of the Society of Dyers and Colourists (UK) 
recommended a coiour difference formula that has been integrated into some ISO standards. 
It is a forerunner to CIE94 and was a model for developing the CIE94 formula. The main 
deviations from CIE94 are found in the weighting factors that are much more complicated 
mathematically in that they contain hue-dependent correction terms. They are defined as 
follows (Clarke etal., 1984): 

S L = 0,040 975 L^/(1 + 0,01 7 65 Lf) t unless L^ < 1 6 when S L = 0,511 
S c = 0,063 8 C* a w!{-\ + 0,013 1 C* abi1 ) + 0,638 
SH = S c (7f+1-/) 
where 

^={(C*ab,l) 4 /[(C*ab,l) 4 + 1900]} 1/2 

7= 0,36 + I 0,4 cos (/) abi1 + 35) | 
unless fr ab1 is between 164° and 345° when 

7=0,56+ | 0,2 cos (/)ab,i +168)1 
The parametric factors are defined as follows: 

k t = l 

k Q ~c 

*h=1 

The parametric factors are mostly chosen c = 1 and / varied between 1 and 2. The 
choice of / and c must be indicated by setting the right numbers in the name of the formula, 
e.g. for textiles a choice of CMC(2:1) is in common use. 

CIE recommends the use of the CIEDE2000 formula whenever in the past the CIE 94 
or CMC formula were used XiX 

Appendix A.6. DIN99 coiour difference formuia 

The preceding colour difference formulae including the CIEDE2000 coiour difference formula 
are non-vectorial transformations from CIELAB space, and do not define a space for colour 
differences. A new formula for colour differences was developed to cope with this problem: 
the DIN99 colour difference formula published in DIN 6176 Coforimetric determination of 
colour differences of surface colours using the DIN 99 formula (DIN, 2003). 



References 

CIE, 1993. CIE 101-1993. Parametric effects in coiour difference evaluation, 1993. 

CIE, 1995. CIE 116-1995. industrial coiour difference evaluation, 1995. 

CLARKE, F.J.J. , MCDONALD, R. and RIGG, B., 1984. Modification to the JPC79 colour 
difference formula. J.Soc.Dyers Col. 100, 128-131, 1984. 

DIN, 2003. DIN 6176. Colorimetric determination of colour differences of surface colours 
using the DIN 99 formula, 2003. 



XiX The recommended use of CIEDE2000 is in agreement with the persons who developed 
the CMC formula. 



54 



CIE 15:2004 



APPENDIX B. DEFINITIONS OF THE 7{A\ g(A), b(A ) COLOUR-MATCHING FUNCTIONS, 
THE CIE RGB SYSTEM AND THE DERIVATION OF THE CiE XYZ SYSTEM FROM THE 
CIE RGB SYSTEM FOR THE 1931 STANDARD OBSERVER 

The colour-matching functions x{A),y(A), z(A) were originally derived from colour-matching 
functions 7(X),g{A) 1 b(A:) referring to spectral reference stimuli [R], [G], [B]. These reference 
stimuli were specified as stimuli of wavelengths 700,0 nm, 546,1 nm, and 435,8 nm, 
respectively. Their units were chosen to make a mixture of equal quantities of the three 
reference stimuli match the equi-energy spectrum. The luminances of the units of the three 
spectral stimuli were in the ratios 1 ,0000 : 4,5907 : 0,0601 . 

Appendix B.1. Determination of the 7(A), g(l), b(A) colour-matching functions 

This determination results from two conventions originally adopted in 1931 . 

The first convention was to adopt the ratios of the luminance of the reference colour 
stimuli [R], [G], [B] as values. 

The second convention was to attribute to the monochromatic stimuli constituting the 
colour-matching functions a luminance equal to the spectral luminous efficiency V(A). 

It follows from these conventions that 

1 ,0000 7(X) + 4,5907 g(A) + 0,0601 b(A) = V(A) B.1 

Since for any stimulus 

R/r=G/g = B/b = L/l B.2 

where / is the characteristic luminance of the chromaticity whose expression for 
monochromatic stimuli reads 

((A) = 1 ,00000 r{A) + 4,5907 g(A) + 0,0601 b(A) B.3 

it follows that, with L = V(A) 

7(A) = [ftA)V(A)]/l(Al g(X) = [g(A)V(A)]HW, b(A)=[b(AJV(A)]/l(Al B.4 

These colour-matching functions as well as the corresponding chromaticity 
coordinates, are given in Table B.1 . 

The colour-matching functions x(A), y(A), z(?J) given in Table T.4 agree closely 
with those defined originally in 1931. Three minor changes have been introduced. If rounded 
to four decimal places, at A =775 nm the new value of x(2)is 0,0001 instead of 0,0000; at 

A- 555 nm y(A)is 1,0000 instead of 1,0002; and at A - 740 nm y(A)\$ 0,0002 instead of 
0,0003. These changes are considered insignificant in most colorimetric calculations. 

It has been realized at an early stage that the 1924 V(A) function is too low in the blue 
part of the spectrum, A corrected V M (A) function has been officially accepted by the CIE in 
1988 (CIE, 1990). However, the X(A), Y(A), Z(A) colour-matching functions have not been 
modified. A CIE Technical Committee is currently investigating the question of obtaining 
visually meaningful colour-matching functions, see e.g. (Schanda, 1998). 



55 



CIE 15:2004 



Appendix B.2. Derivation of the CIE XYZ trichromatic system from the CIE RGB 
trichromatic system 

The derivation of the XYZ system from the RGB system had to fulfil a certain number of 
requirements. Their fulfilment led to the establishment of a set of three linear equations 
relating the reference stimuli [X], [Y], [Z] to the reference stimuli [R], [G], [B] as follows: 

[X] = 0,418 455 [R] - 0,091 165 [G] + 0,000 921 [B] 

[Y] = -0,158 657 [R] + 0,252 426 [G] - 0,002 550 [B] B.5 

[Z] = -0 ; 082 832 [R] + 0,015 705 [G] +0,178 595 [B] 

Another set of three linear equations yield, for any stimulus, the tristimulus values X, 
Y, Z as function of the tristimulus values R, G, B: 

X= 2,768 892 R + 1,751 748 G + 1,130 160 B 

Y = 1 ,000 000 R + 4,590 700 G + 0,060 1 00 B B.6 

Z = + 0,056 508 G + 5,594 292 B 

These sets B. 5 and B. 6 are not independent, each one may be mathematically 
derived from the other. The set B. 6 was developed first and its coefficients are exact values 
(Morren, 2000), This set may be considered as more appropriate in the present context, but 
the set B. 5 is more basic, Since colour-matching functions are a particular case of tristimulus 
values, the set B. 6 gives directly three equations providing x(A), y(X), z(A) as a function of 

The second of these equations: 

y(A) =1,000 000 r(A) + 4,590 700 g(X) + 0,060 100 b{A) 

is particularly interesting: it reproduces the left-hand side of equation B. 1 under Section B. 1 
and thus immediately leads to y{X) = V(A). 

Note: However, the same conclusion may be obtained by considering other features of the 
XYZ system. The transformation between reference stimuli attributes to the 
luminance L Y the value 1. Moreover, since the reference stimuli [X] and [Z] are 
located on the alychne of the system, leading to L x = L z = 0, one has for any stimulus 

L = Y and l-y B.7 

Consequently, equations similar to B. 4 lead to 

x(/)=[x(l).l/(l)]/yW, y(X) = V(Al z(A) - [z(l)-\/(A)]/y(A) B.8 

These expressions are simpler than those given by the set B. 6. 

In deriving the CIE XYZ colorimetric system a fundamental criterion was to link the 
system to photometry. The units of the RGB system, the RGB primaries, were already 
determined by their luminance. Furthermore this was done by using a transformation from the 
RGB system to the XYZ system where y(Z) became equivalent to V(A), determined by flicker 
photometry. Although y(X) was intended to be a brightness correlate, it is actually a 

luminance correlate, i.e. it does not describe the brightness relationship between coloured 
lights. It does, however, provide a good estimate for the visibility of fine detail. 



56 



CI E 15:2004 

Appendix B.3. Definition of the colour-matching functions in the CIE 1964 trichromatic 
system 

The colour-matching functions x 10 (A), y 10 W, *ioW deff n ' n 9 the CIE 1964 standard 
coiorimetric observer given in Table T.5 were derived from colour-matching functions referring 
to matching stimuli [R 10 ], [G 10 ], [B 10 ]. These are stimuli specified in terms of wavenumbers (v) 
15 500 cm" 1 , 19 000 cm" 1 , and 22 500 cm" 1 (corresponding approximately to wavelengths 
645,2 nm, 526,3 nm, and 444,4 nm), and their amounts are given in power units. 

The three reference stimuli [R 10 ], [G 10 J, [B 10 ] have the same power and the colour- 
matching functions r 10 (v), g<\ (v), b w (v) are defined as monochromatic stimuli whose power 
equates to that of the reference stimuli. The r 10 (v) , g 10 (v) , j£) 10 (v) colour matching functions 
are reproduced in Table B.2. 

The derivation of the [X 10 ], [Y 10 ], [Z 10 ] system from the [R 10 ], [G 10 ], [B 10 ] system is 
based on principles that lead to a coordinate system similar to the system associated with the 
CIE 1931 standard coiorimetric observer. The following transformation equations relate very 
closely the r 10 (v), g 10 M, b w (v) values of Table B. 2 to x 10 (k), y 10 (v), z 10 (v) values: 

x 10 (v) = 0,341 080 r 10 (v) + 0,189 145 g 10 (v) + 0,387 529 b 10 (v) 
y 10 (v) - 0,139 058 r 10 (v) + 0,837 460 g 10 (v) + 0,073 316 b w (v) 
z 10 (v) - 0,000 000 r 10 (w) + 0,039 553 g 10 (v) 4 2,026 200 b w (v) 

Chromaticity coordinates x 10 (v), yi ( v), z^(v) were then computed from 
x 10 M= * 1oM 



^oM+yioM+^oM 

y 10 (v)= M 

^oM + yioM + ^oM 



z 10 (v) 



Table 2 of CIE standard coiorimetric observers (CIE, 1986) contains the official 
colour-matching functions x 10 (/l) , y 10 (A), z 10 (^) and chromaticity coordinates x 10 (^) t y 10 (^), 
z 10 (/L) on a wavelength basis obtained by interpolation and extrapolation of the functions 
XioM - 7io(^) ' *ioM and x io(^). yioU), z 10 (/t) at intervals of 1 nm. Table T.5 contains every 
fifth value of this table. 

The above transformation equations deviate somewhat from those originally 
published (CIE, 1959), which related the unsmoothed values of r w (v), g 10 (v), b 10 (v) with 
the unsmoothed values of x 10 (A) , y 10 (^) , z w (Jl) . The values published in CIE 15.2 (Table 
2.6) are reproduced in this Appendix as Table B. 2. 

In deriving the CIE 1964 standard coiorimetric observer no direct photometric 
measurements were required. The large-field colour matching data as defined by the CIE 
1964 standard coiorimetric observer are intended to apply to matches where the luminance 
and relative spectral power distributions of the matched stimuli are such that no participation 
of the rod receptors of the visual mechanism is to be expected. This condition of observation 
is important as "rod intrusion" may upset the predictions of the standard observer. 

In obtaining the RGB-XYZ transformation CIE tried to get the y 10 (^) function as near 
as possible to a 10 degree spectral luminosity function based on flicker photometry. The CIE 
is currently investigating the possibility of introducing on this basis a V^ (X) function. 



57 



CIE 15:2004 



Table B.1 . Colour-matching functions r(X ), g{ X ), b(X ) and corresponding chromaticity 

coordinates r{A), 9(a), b(X) for wavelength 380 nm to 780 nm at 5 nm intervals for 
the 1931 standard observer. 



X, nm 


7(X) 


9W 


b(X) 


tXX) 


gU) 


b(X) 


380 


0,00003 


-0,00001 


0,00117 


0,0272 


-0,0115 


0,9843 


385 


0,00005 


-0,00002 


0,00189 


0,0268 


-0,0114 


0,9846 


390 


0,00010 


-0,00004 


0,00359 


0,0263 


-0,0114 


0,9851 


395 


0,00017 


-0,00007 


0,00647 


0,0256 


-0,0113 


0,9857 


400 


0,00030 


-0,00014 


0,01214 


0,0247 


-0,0112 


0,9865 


405 


0,00047 


-0,00022 


0,01969 


0,0237 


-0,01 1 1 


0,9874 


410 


0,00084 


-0,00041 


0,03707 


0,0225 


-0,0109 


0,9884 


415 


0,00139 


-0,00070 


0,06637 


0,0207 


-0,0104 


0,9897 


420 


0,00211 


-0,00110 


0,11541 


0,0181 


-0,0094 


0,9913 


425 


0,00266 


-0,00143 


0,18575 


0,0142 


-0,0076 


0,9934 


430 


0,00218 


-0,00119 


0,24769 


0,0088 


-0,0048 


0,9960 


435 


0,00036 


-0,00021 


0,29012 


0,0012 


-0,0007 


0,9995 


440 


-0,00261 


0,00149 


0,31228 


-0,0084 


0,0048 


1,0036 


445 


-0,00673 


0,00379 


0,31860 


-0,0213 


0,0120 


1,0093 


450 


-0,01213 


0,00678 


0,31670 


-0,0390 


0,0218 


1,0172 


455 


-0,01874 


0,01046 


0,31166 


-0,0618 


0,0345 


1,0273 


460 


-0,02608 


0,01485 


0,29821 


-0,0909 


0,0517 


1,0392 


465 


-0,03324 


0,01977 


0,27295 


-0,1281 


0,0762 


1,0519 


470 


-0,03933 


0,02538 


0,22991 


-0,1821 


0,1175 


1,0646 


475 


-0,04471 


0,03183 


0,18592 


-0,2584 


0,1840 


1,0744 


480 


-0,04939 


0,03914 


0,14494 


-0,3667 


0,2906 


1,0761 


485 


-0,05364 


0,04713 


0,10968 


-0,5200 


0,4568 


1,0632 


490 


-0,05814 


0,05689 


0,08257 


-0,7150 


0,6996 


1,0154 


495 


-0,06414 


0,06948 


0,06246 


-0,9459 


1 ,0247 


0,9212 


500 


-0,07173 


0,08536 


0,04776 


-1,1685 


1,3905 


0,7780 


505 


-0,08120 


0,10593 


0,03688 


-1,3182 


1,7195 


0,5987 


510 


-0,08901 


0,12860 


0,02698 


-1,3371 


1,9318 


0,4053 


515 


-0,09356 


0,15262 


0,01842 


-1,2076 


1,9699 


0,2377 


520 


-0,09264 


0,17468 


0,01221 


-0,9830 


1,8534 


0,1296 


525 


-0,08473 


0,19113 


0,00830 


-0,7386 


1,6662 


0,0724 


530 


-0,07101 


0,20317 


0,00549 


-0,5159 


1 ,4761 


0,0398 


535 


-0,05316 


0,21083 


0,00320 


-0,3304 


1,3105 


0,0199 


540 


-0,03152 


0,21466 


0,00146 


-0,1707 


1,1628 


0,0079 


545 


-0,00613 


0,21487 


0,00023 


-0,0293 


1,0282 


0,0011 


550 


0,02279 


0,21178 


-0,00058 


0,0974 


0,9051 


-0,0025 


555 


0,05514 


0,20588 


-0,00105 


0,2121 


0,7919 


-0,0040 


560 


0,09060 


0,19702 


-0,00130 


0,3164 


0,6881 


-0,0045 


565 


0,12840 


0,18522 


-0,00138 


0,4112 


0,5932 


-0,0044 


570 


0,16768 


0,17087 


-0,00135 


0,4973 


0,5067 


-0,0040 


575 


0,20715 


0,15429 


-0,00123 


0,5751 


0,4283 


-0,0034 


580 


0,24526 


0,13610 


-0,00108 


0,6449 


0,3579 


-0,0028 



58 



CiE 15:2004 



A, nm 


7W 


9tt) 


b{X) 


M) 


SM 


b{X) 


585 


0,27989 


0,11686 


-0,00093 


0,7071 


0,2952 


-0,0023 


590 


0,30928 


0,09754 


-0,00079 


0,7617 


0,2402 


-0,0019 


595 


0,33184 


0,07909 


-0,00063 


0,8087 


0,1928 


-0,0015 


600 


0,34429 


0,06246 


-0,00049 


0,8475 


0,1537 


-0,0012 


605 


0,34756 


0,04776 


-0,00038 


0,8800 


0,1209 


-0,0009 


610 


0,33971 


0,03557 


-0,00030 


0,9059 


0,0949 


-0,0008 


615 


0,32265 


0,02583 


-0,00022 


0,9265 


0,0741 


-0,0006 


620 


0,29708 


0,01828 


-0,00015 


0,9425 


0,0580 


-0,0005 


625 


0,26348 


0,01253 


-0,00011 


0,9550 


0,0454 


-0,0004 


630 


0,22677 


0,00833 


-0,00008 


0,9649 


0,0354 


-0,0003 


635 


0,19233 


0,00537 


-0,00005 


0,9730 


0,0272 


-0,0002 


640 


0,15968 


0,00334 


-0,00003 


0,9797 


0,0205 


-0,0002 


645 


0,12905 


0,00199 


-0,00002 


0,9850 


0,0152 


-0,0002 


650 


0,10167 


0,00116 


-0,00001 


0,9888 


0,0113 


-0,0001 


655 


0,07857 


0,00066 


-0,00001 


0,9918 


0,0083 


-0,0001 


660 


0,05932 


0,00037 


0,00000 


0,9940 


0,0061 


-0,0001 


665 


0,04366 


0,00021 


0,00000 


0,9954 


0,0047 


-0,0001 


670 


0,03149 


0,00011 


0,00000 


0,9966 


0,0035 


-0,0001 


675 


0,02294 


0,00006 


0,00000 


0,9975 


0,0025 


0,0000 


680 


0,01687 


0,00003 


0,00000 


0,9984 


0,0016 


0,0000 


685 


0,01187 


0,00001 


0,00000 


0,9991 


0,0009 


0,0000 


690 


0,00819 


0,00000 


0,00000 


0,9996 


0,0004 


0,0000 


695 


0,00572 


0,00000 


0,00000 


0,9999 


0,0001 


0,0000 


700 


0,00410 


0,00000 


0,00000 


1,0000 


0,0000 


0,0000 


705 


0,00291 


0,00000 


0,00000 


1,0000 


0,0000 


0,0000 


710 


0,00210 


0,00000 


0,00000 


1,0000 


0,0000 


0,0000 


715 


0,00148 


0,00000 


0,00000 


1,0000 


0,0000 


0,0000 


720 


0,00105 


0,00000 


0,00000 


1,0000 


0,0000 


0,0000 


725 


0,00074 


0,00000 


0,00000 


1,0000 


0,0000 


0,0000 


730 


0,00052 


0,00000 


0,00000 


1,0000 


0,0000 


0,0000 


735 


0,00036 


0,00000 


0,00000 


1,0000 


0,0000 


0,0000 


740 


0,00025 


0,00000 


0,00000 


1,0000 


0,0000 


0,0000 


745 


0,00017 


0,00000 


0,00000 


1,0000 


0,0000 


0,0000 


750 


0,00012 


0,00000 


0,00000 


1,0000 


0,0000 


0,0000 


755 


0,00008 


0,00000 


0,00000 


1,0000 


0,0000 


0,0000 


760 


0,00006 


0,00000 


0,00000 


1,0000 


0,0000 


0,0000 


765 


0,00004 


0,00000 


0,00000 


1,0000 


0,0000 


0,0000 


770 


0,00003 


0,00000 


0,00000 


1,0000 


0,0000 


0,0000 


775 


0,00001 


0,00000 


0,00000 


1,0000 


0,0000 


0,0000 


780 


0,00000 


0,00000 


0,00000 


1,0000 


0,0000 


0,0000 



59 



CIE 15:2004 

Table B.2. CIE 1964 standard colorimetric observer. Colour-matching functions r 10 (v), 
9w(v), b 10 (v) and corresponding chromaticity coordinates r 10 (v), gio(v), bi (v) 
for wavenumbers v- 27 750 to 12 250 cm" 1 at 250 cm" 1 intervals. 



v, cm" 1 


^ (y) 


ShoM 


bioM 


fio(v) 


0io(v) 


b :o (y) 


27750 


0,000000079100 


-0,000000021447 


0,000000307299 


0,21674 


-0,05877 


0,84203 


27500 


0,00000029891 


-0,00000008125 


0,00000116475 


0,21622 


-0,05877 


0,84255 


27250 


0,00000108348 


-0,00000029533 


0,00000423733 


0,21560 


-0,05877 


0,84317 


27000 


0,0000037522 


-0,0000010271 


0,0000147506 


0,21471 


-0,05877 


0,84406 


26750 


0,0000123776 


-0,0000034057 


0,0000489822 


0,21358 


-0,05877 


0,84519 


26500 


0,000038728 


-0,000010728 


0,000154553 


0,21215 


-0,05877 


0,84662 


26250 


0,000114541 


-0,000032004 


0,000462055 


0,21032 


-0,05877 


0,84844 


26000 


0,00031905 


-0,00009006 


0,00130350 


0,20819 


-0,05877 


0,85058 


25750 


0,00083216 


-0,00023807 


0,00345702 


0,20542 


-0,05877 


0,85335 


25500 


0,00201685 


-0,00058813 


0,00857776 


0,20155 


-0,05877 


0,85722 


25250 


0,0045233 


-0,0013519 


0,0198315 


0, 1 9664 


-0,05877 


0,86213 


25000 


0,0093283 


-0,0028770 


0,0425057 


0,19054 


-0,05877 


0,86823 


24750 


0,0176116 


-0,0056200 


0,0840402 


0,18339 


-0,05852 


0,87513 


24500 


0,030120 


-0,010015 


0,152451 


0,17455 


-0,05804 


0,88349 


24250 


0,045571 


-0,016044 


0,251453 


0,16219 


-0,05710 


0,89491 


24000 


0,060154 


-0,022951 


0,374271 


0,14619 


-0,05578 


0,90959 


23750 


0,071261 


-0,029362 


0,514950 


0,12797 


-0,05273 


0,92476 


23500 


0,074212 


-0,032793 


0,648306 


0,10760 


-0,04755 


0,93995 


23250 


0,068535 


-0,032357 


0,770262 


0,08498 


-0,04012 


0,95514 


23000 


0,055848 


-0,027996 


0,883628 


0,06127 


-0,03071 


0,96944 


22750 


0,033049 


-0,017332 


0,965742 


0,03367 


-0,01766 


0,98399 


22500 


0,000000 


0,000000 


1,000000 


0,00000 


0,00000 


1 ,00000 


22250 


-0,041570 


0,024936 


0,987224 


-0,04283 


0,02569 


1,01714 


22000 


-0,088073 


0,057100 


0,942474 


-0,09662 


0,06264 


1 ,03398 


21750 


-0,143959 


0,099886 


0,863537 


-0,17567 


0,12189 


1,05378 


21500 


-0,207995 


0,150955 


0,762081 


-0,29501 


0,21411 


1,08090 


21250 


-0,285499 


0,218942 


0,630116 


-0,50660 


0,38850 


1,11810 


21000 


-0,346240 


0,287846 


0,469818 


-0,84156 


0,69963 


1,14193 


20750 


-0,388289 


0,357723 


0,333077 


-1,28355 


1,18251 


1,10104 


20500 


-0,426587 


0,435138 


0,227060 


-1,81056 


1,84685 


0,96371 


20250 


-0,435789 


0,513218 


0,151027 


-1,90754 


2,24646 


0,66108 


20000 


-0,438549 


0,614637 


0,095840 


-1,61274 


2,26029 


0,35245 


19750 


-0,404927 


0,720251 


0,057654 


-1,08566 


1,93108 


0,15458 


19500 


-0,333995 


0,830003 


0,029877 


-0,63511 


1,57830 


0,05681 


19250 


-0,201889 


0,933227 


0,012874 


-0,27128 


1,25398 


0,01730 


19000 


0,000000 


1,000000 


0,000000 


0,00000 


1,00000 


0,00000 


18750 


0,255754 


1,042957 


-0,008854 


0,19828 


0,80858 


-0,00686 


18500 


0,556022 


1,061343 


-0,014341 


0,34686 


0,66209 


-0,00895 


18250 


0,904637 


1,031339 


-0,017422 


0,47152 


0,53756 


-0,00908 


18000 


1,314803 


0,976838 


-0,018644 


0,57844 


0,42976 


-0,00820 


17750 


1,770322 


0,887915 


-0,017338 


0,67035 


0,33622 


-0,00657 


17500 


2,236809 


0,758780 


-0,014812 


0,75041 


0,25456 


-0,00497 


17250 


2,641981 


0,603012 


-0,011771 


0,81714 


0,18650 


-0,00364 


17000 


3,002291 


0,452300 


-0,008829 


0,87130 


0,13126 


-0,00256 



60 



CiE 15:2004 



v, cm" 1 


'io(v) 


flhoM 


M") 


Tio(K) 


0io(v) 


Jbio(v) 


16750 


3,159249 


0,306869 


-0,005990 


0,91304 


0,08869 


-0,00173 


16500 


3,064234 


0.184057 


-0,003593 


0,94438 


0,05673 


-0,00111 


16250 


2,717232 


0,094471 


-0,001844 


0,96704 


0,03362 


-0,00066 


16000 


2,191156 


0,041693 


-0,000815 


0,98169 


0,01868 


-0,00037 


15750 


1,566864 


0,013407 


-0,000262 


0,99168 


0,00849 


-0,00017 


15500 


1 .000000 


0,000000 


0,000000 


1,00000 


0,00000 


0,00000 


15250 


0,575756 


-0,002747 


0,000054 


1,00470 


-0,00479 


0,00009 


15000 


0,296964 


-0,002029 


0,000040 


1,00674 


-0,00688 


0,00014 


14750 


0,138738 


-0,001116 


0,000022 


1,00795 


-0,00811 


0,00016 


14500 


0,0602209 


-0,0005130 


0,0000100 


1,00842 


-0,00859 


0,00017 


14250 


0,0247724 


-0,0002152 


0,0000042 


1,00859 


-0,00876 


0,00017 


14000 


0,00976319 


-0,00008277 


0,00000162 


1,00838 


-0,00855 


0,00017 


13750 


; 00375328 


0,00003012 


0,00000059 


1,00793 


-0,00809 


0,00016 


13500 


0,00141908 


-0,00001051 


0,00000021 


1,00731 


-0,00746 


0,00015 


13250 


0,000533169 


-0,000003543 


0,000000069 


1,00656 


-0,00669 


0,00013 


13000 


0,000199730 


-0,000001144 


0,000000022 


1,00565 


-0,00576 


0,00011 


12750 


0,0000743522 


-0,0000003472 


0,0000000068 


1,00460 


-0,00469 


0,00009 


12500 


0,0000276506 


-0,0000000961 


0,0000000019 


1,00342 


-0,00349 


0,00007 


12250 


0,0000102123 


-0,0000000220 


0,0000000004 


1,00212 


-0,00216 


0,00004 



Reference 

CiE, 1959. Proc. of the 14th Session of CIE, Brussels, Vol. A, 91-109, 1959. 

CIE. 1986. CIE S002-1986. CIE standard coiorimetric observers, 1986. (Published also as 
CIE/ISO 10527:1991). 

CIE, 1990. CIE 86-1990. CIE 1988 2° spectral luminous efficiency function for photopic vision, 
1990. 

MORREN L, 2000. Private communication, calculations done for the CIE TC 1-48. 

SCHANDA, J., 1998. Current CIE work to achieve physiologically correct colour metrics, in 
Color Vision, Perspectives from different disciplines, eds.: Backhaus, W.G.K., Kliegl, R., 
Werner, J.S. Walter de Gruyter, Berlin- New York, 1998. 



61 



C1E 15:2004 



APPENDIX C. ALTERNATIVE METHOD TO DEFINE DAYLIGHT ILLUMINANTS - 
METHOD OF CALCULATION, CORRECTED TABLES AND EQUATIONS (FOR 
INFORMATION AND EVALUATION) 

If one tries to apply the calculation procedure for other illuminants D, which is described in 
Section 3.1 to D65, one has to follow a rounding process for computing the coefficients M^ 
and M 2 and then a peculiar practice for rounding the final results. These unusual procedures 
explain the slight deviations sometimes observed in comparison with the official table for 
standard illuminant D65. These changes are negligible for colorimetric calculations, but are 
annoying if tables are compared, see (Kranicz and Schanda, 2000). 

Daylight illuminant spectral power distribution tables are based on the work of Judd 
and co-workers (Judd et aL, 1964), who proposed the calculation method of daylight 
illuminants based on the S , S 1f S 2 component functions. Judd and co-workers published the 
So, Si, S 2 functions at 10 nm increments: from these the table accepted by the CIE and 
reproduced in Table T.2 was calculated using linear interpolation. (Also Table 1 of the CIE 
standard (CIE, 1998) was calculated using linear interpolation.) 

Using the equations in Section 3.1 without following carefully the details of use may 
lead to slightly different results if the original 10 nm tables, or the 5 nm tables as reproduced 
in Section 11. Tables, or the 1 nm tables of the standard are used. To overcome this problem 
- and to harmonise colorimetric practice - an alternative method is recommended for 
evaluation. Since the interpolation of all other colorimetric functions from their original 10 nm 
values has been done by non-linear interpolation, these new tables have been derived by a 
Lagrange interpolation method**. The table containing the Lagrange interpolated S 0L a g) S 1Lag 
and S 2L ag values of the S 0l S 1f S 2 functions at 1 nm increments is included on the 
accompanying CD-ROM. The original Judd and co-workers' 10 nm data were used as input 
data. Table C 1 shows the 5 nm sampled set of values. 

The starting point for Daylight Illuminant calculation is the set of Equ.'s 3.2, 3.3 and 
3.4 of the main publication. 

First one has to calculate the x D chromaticity coordinate of the daylight phase 
required using Equ. 3.3 for daylight illuminant correlated colour temperatures from 
approximately 4000 K to 7000 K, or Equ. 3.4 for daylight illuminant correlated colour 
temperatures from larger than 7000 K to approximately 25 000 K. 

Then y D is calculated using Equ. 3.2. 

These Equ.'s are regarded as defining the daylight chromaticity. 

The next step is to calculate the Daylight Illuminant relative spectral power distribution 
using these x D , y D values and Equ. 3.5: XXI 

S(A) = So(Z) + M,SM) + M 2 S 2 (A) (3.5) 

The official CIE method uses the S (A), Si (A), S 2 (X) functions as defined in Table T.2. 
These component spectra were originally determined at the full 10 nm increments, and later 
linearly interpolated to every 5 nm. 

To calculate S(A) one has to know the M u M 2 factors. The original Judd publication 
defines these as functions of x D , y D as reproduced in Equ. 3.6: XXI 

_ -1,351 5 -1,7703x D + 5,91 14y D 
1 ~ 0,0241 + 0,2562x D - 0,7341y D (3 6) 

.. 0,030 - 31,4424 x D +30,071 7y D 

2 



0,0241 + f 2562x D - 0,734 1y D 



xx To be able to determine S , S u S 2 values at any desired wavelength, the accompanying 
CD-ROM contains a Lagrange interpolation program. 



XXI 



Equ.'s 3.5 and 3.6 are taken from Section 3 of the present document. 



62 



CI E 15:2004 



The constants in these Equ.'s depend, however, on the sampling of the S functions, 
see (Kranicz and Schanda, 2000). The main publication overcomes this difficulty by stating 
that calculations have to be done at 10 nm increments with subsequent linear interpolation. 

The M 1( M 2 functions can be written in a general form: 

M _ gn*D+ft n yD+''n 



jx D + ky D + / 
where n = 1 for Equ. M-, and n = 2 for Equ. M 2 . 

g, h, i, I k and / are obtained as the tristimulus values of the S (A), $i(/l), S 2 (A) 
functions, and recommended values are listed in Table C 2. Thus e.g. 

gi =10QO B ° D2 " B2Do 



D 2 



where e.g. 



B = £s U)yU)AA and B 2 = Js 2 U) y(l)AA 



Anin 



and the D symbols refer to the sum of the three tristimulus values of the form as shown by the 
B equations for the /tristimulus values of the S , Si and S 2 functions. 

The tristimulus values will depend on the method of summation, and thus also the g, 
h, i, I k and / coefficients will depend on them. This ultimately will have an influence on the x s , 
y s chromaticity coordinates of the daylight phases calculated from the S(Z) spectral power 
distribution according to Equ. 3.5. If these x s , y s values deviate from the x D , y D values used as 
the input values in the calculation, a user may feel unsure as to whether he or she has 
followed the procedure correctly. To avoid such confusion, values of g n , h n , i n , j, k and / have 
to be calculated for the summation used for calculating S(A). Table C.2 shows the 
recommended values for the CIE 1931 and CIE 1964 standard observers using the 1 nm 
standard tables and the Lagrange interpolated S 0Lag , S 1Lag , S 2 L ag tables, both for 1 nm and 5 
nm abridged and truncated colour matching tables. Using these g^ ... i coefficients the x Si ys 
values agree with the x D , y D values to five decimal places. 



63 



CiE 15:2004 



Table C.1. S 0L ag, S 1Lag and S 2L ag 5 nm sampled spectra. 



X, nm 


SoLag 


SiLag 


S2Lsg 


300 


0,04000 


0,02000 


0,00000 


305 


-0,15625 


-0,15000 


1,15625 


310 


6,00000 


4,50000 


2,00000 


315 


16,56625 


12,50500 


2,84375 


320 


29,60000 


22,40000 


4,00000 


325 


43,80000 


33,40625 


6,41875 


330 


55,30000 


42,00000 


8,50000 


335 


57,62500 


42,46250 


8,50000 


340 


57,30000 


40,60000 


7,80000 


345 


59,69375 


41,23750 


7,29375 


350 


61,80000 


41,60000 


6,70000 


355 


61,47500 


39,58750 


5,88125 


360 


61,50000 


38,00000 


5,30000 


365 


65,46875 


40,21875 


5,80625 


370 


68,80000 


42,40000 


6,10000 


375 


66,40625 


40,94375 


4,71250 


380 


63,40000 


38,50000 


3,00000 


385 


62,45000 


35,98125 


2,05000 


390 


65,80000 


35,00000 


1,20000 


395 


79,82500 


38,80000 


-0,10000 


400 


94,80000 


43,40000 


-1,10000 


405 


101,54375 


45,52500 


-0,93125 


410 


104,80000 


46,30000 


-0,50000 


415 


106,54375 


45,70625 


-0,53125 


420 


105,90000 


43,90000 


-0,70000 


425 


100,35000 


40,37500 


-0,87500 


430 


96,80000 


37,10000 


-1,20000 


435 


104,05000 


36,52500 


-1,91250 


440 


113,90000 


36,70000 


-2,60000 


445 


120,82500 


36,48125 


-2,84375 


450 


125,60000 


35,90000 


-2,90000 


455 


126,54375 


34,49375 


-2,88125 


460 


125,50000 


32,60000 


-2,80000 


465 


123,39375 


30,26875 


-2,69375 


470 


121,30000 


27,90000 


-2,60000 


475 


121,52500 


26,06875 


-2,63750 


480 


121,30000 


24,30000 


-2,60000 


485 


117,42500 


22,21875 


-2,21875 



X, nm 


SoLag 


$1Lag 


S 2 |_sg 


490 


113,50000 


20,10000 


-1,80000 


495 


112,95625 


18,07500 


-1,61250 


500 


113,10000 


16,20000 


-1,50000 


505 


112,19375 


14,74375 


-1,38750 


510 


110,80000 


13,20000 


-1,30000 


515 


108,36250 


10,86875 


-1,25000 


520 


106,50000 


8,60000 


-1,20000 


525 


107,60000 


7,18125 


-1,12500 


530 


108,80000 


6,10000 


-1,00000 


535 


107,25000 


5,13750 


-0,75000 


540 


105,30000 


4,20000 


-0,50000 


545 


104,90625 


3,05000 


-0,38750 


550 


104,40000 


1,90000 


-0,30000 


555 


102,39375 


0,90625 


-0,15000 


560 


100,00000 


0,00000 


0,00000 


565 


97,78125 


-0,80000 


0,10000 


570 


96,00000 


-1,60000 


0,20000 


575 


95,67500 


-2,65000 


0,26250 


580 


95,10000 


-3,50000 


0,50000 


585 


91,95625 


-3,47500 


1,25000 


590 


89,10000 


-3,50000 


2,10000 


595 


89,43750 


-4,56250 


2,69375 


600 


90,50000 


-5,80000 


3,20000 


605 


90,60625 


-6,55625 


3,68125 


610 


90,30000 


-7,20000 


4,10000 


615 


89,61250 


-7,93125 


4,43125 


620 


88,40000 


-8,60000 


4,70000 


625 


86,01250 


-9,05000 


4,83750 


630 


84,00000 


-9,50000 


5,10000 


635 


84,47500 


-10,26875 


5,88750 


640 


85,10000 


-10,90000 


6,70000 


645 


83,52500 


-10,80625 


7,01875 


650 


81,90000 


-10,70000 


7,30000 


655 


81,90625 


-11,21250 


7,91250 


660 


82,60000 


-12,00000 


8,60000 


665 


84,01875 


-13,10625 


9,25625 


670 


84,90000 


-14,00000 


9,80000 


675 


83,83125 


-14,02500 


10,19375 



64 



CIE 15:2004 



X, nm 


^OLag 


Snag 


$2Lsg 


680 


81,30000 


-13,60000 


10,20000 


685 


76,22500 


-12,69375 


9,19375 


690 


71,90000 


-12,00000 


8,30000 


695 


72,38125 


-12,57500 


8,90000 


700 


74,30000 


-13,30000 


9,60000 


705 


76,31875 


-13,32500 


9,22500 


710 


76,40000 


-12,90000 


8,50000 


715 


69,45625 


-11,66250 


7,64375 


720 


63,30000 


-10,60000 


7,00000 


725 


66,35000 


-10,91875 


7,18125 


730 


71,70000 


-11,60000 


7,60000 


735 


75,61250 


-12,08750 


7,91875 


740 


77,00000 


-12,20000 


8,00000 


745 


72,52500 


-11,38750 


7,46875 


750 


65,20000 


-10,20000 


6,70000 


755 


54,40625 


-8,66250 


5,73125 



X, nm 


£>OLag 


S"ILag 


^2Lsg 


760 


47,70000 


-7,80000 


5,20000 


765 


57,28125 


-9,40000 


6,24375 


770 


68,60000 


-11,20000 


7,40000 


775 


68,04375 


-11,00000 


7,22500 


780 


65,00000 


-10,40000 


6,80000 


785 


65,58750 


-10,50625 


6,90000 


790 


66,00000 


-10,60000 


7,00000 


795 


64,04375 


-10,25000 


6,76875 


800 


61,00000 


-9,70000 


6,40000 


805 


56,48750 


-8,88125 


5,87500 


810 


53,30000 


-8,30000 


5,50000 


815 


55,43125 


-8,68125 


5,71875 


820 


58,90000 


-9,30000 


6,10000 


825 


61,71875 


-9,79375 


6,43125 


830 


61,90000 


-9,80000 


6,50000 



Table C.2. g 1 to / coefficients for CiE 1931 and 1964 standard observers and 1 nm standard 
tables using the Lagrange interpolated S , Si and S 2 functions both for 1 nm and 5 nm 
sampling. 



Coeff.s 


CIE 1931 St. 
Obs. 

1 nm sampling 


CIE 1964 St. 
Obs. 

1 nm sampling 


CIE 1931 St. 
Obs. 

5 nm sampling 


CIE 1964 St. 
Obs. 

5 nm sampling 


Qi 


-1 ,77864 


-1 ,57049 


-1,77861 


-1,57049 


Ai 


5,90745 


5,56450 


5,90757 


5,56460 


/i 


-1,34666 


-1,31211 


-1,34674 


-1,31215 


92 


-31,44505 


-30,15166 


-31,44464 


-30,15139 


h 2 


30,06408 


31,07906 


30,06400 


31,07931 


h 


0,03656 


-0,73912 


0,03638 


-0,73928 


J 


0,25540 


0,21249 


0,25539 


0,21250 


k 


-0,73218 


-0,71591 


-0,73217 


-0,71592 


1 


0,02387 


0,04663 


0,02387 


0,04663 



References 

CIE, 1998. CIES005/E:1998. CIE standard iiluminants for colorimetry. (Published also as ISO 
10526:1999(E)/CIE S 005-1998), 1998. 

JUDD, D.B., MACADAM, D.L. and WYSZECKI, G., 1964. with the collaboration of BUDDE, 
H.W., CONDIT, H.R., HENDERSON, ST, and SIMONDS, J.L Spectral distribution of typical 
daylight as a function of correlated color temperature. J. Opt. Soc. Am. 54, 1031-1040, 1964. 

KRANICZ, B. and SCHANDA, J., 2000. Re-evaluation of daylight spectral distributions. Color 
Res. AppL, 25 (4), 250-259, 2000. 



65 



CiE 15:2004 

APPENDIX D. REVERSE TRANSFORMATION FROM VALUES L*, a*, b* TO 
TRISTIMULUS VALUES X, Y, Z 

In Information Technology (IT) transformations are necessary from the tristimulus values X, Y, 
Z to the values L*,a*,b* and in the reverse [R] direction, Therefore it was decided at the TC 
meetings in Veszprem in August 2002 to include a proposed reverse transformation into CIE- 
Publication 15 "Colorimetry". The first transformations are given in the main part of the 
document (see Section 8.2.1) and the reverse transformations are in this Appendix D. 

Reverse transformation: 

Calculate from the values L*, a*, b* 

/(Y/Yn)=(L*+16)/116 (D.1) 

f(X/Xn)=a*/ 500 +/( Y/Y n ) (D.2) 

f(Z/ZnK(Y/Y n )-jb*/200 (D.3) 

Calculate then the tristimulus values X, Y, Z from: 

X^Xn[/(X/Xn)] 3 if f(X/Xn) > 24/1 16 (D.4) 

X=Xn[fl[X/Xn) - 16/1 16]x(108/841) if f[X/Xn) < 24/1 16 (D.5) 

Y=Yn[/(Y/Yn)] 3 if f[Y!Yn) > 24/1 16 or L*> 8 (D.6) 

Y=Yn[/(Y/Yn)-16/116]x(108/841) if /(Y/Yn) < 24/116 or L*< 8 (D.7) 

Z=Zn[/(Z/Zn)] 3 if /(Z/Zn) > 24/116 (D.8) 

Z=Zn[/{Z/Zn) - 16/11 6]x( 108/841) if /(Z/Zn) < 24/116 (D.9) 



Note: Integer ratios, e. g. 16/116, 841/108, 108/841, are used for both transformations to 
avoid rounding errors. The break point between the non-linear and the linear part of 
the values L* is at L* =8 as proposed by Pauli (1976). 



Reference 

PAUL!, H., 1976. Proposed extension of the CIE recommendation on "Uniform color spaces, 
color difference equations, and metric color terms". J. Opt. Soc. Am., 66, 866-867, 1976. 



66 



CIE 15:2004 



APPENDIX E. INFORMATION ON THE USE OF PLANCK'S EQUATION FOR STANDARD 
AIR 

According to the Planck's law, the spectra! radiance of a blackbody at thermodynamic 
temperature 7"[K] in a medium having index of refraction n is given by 



^ r >=°^ 



exp i^h 



(E.1) 



where c^ = 2%hc 2 , c 2 - hclk, h is Planck's constant, c is the speed of light in vacuum, k is the 
Boitzmann constant, and k is the wavelength in the medium. Since T is measured on the 
International Temperature Scale, the value of c 2 used in colorimetry should follow that 
adopted in the current international Temperature Scale (ITS-90) (Preston-Thomas, 1990; 
Mielenz et al., 1991), namely c 2 - 1,4388 x 10" 2 m K. The official value of c^ is provided by the 
Committee on Data for Science and Technology (CODATA), and is d = 3,741 771 x 10" 16 
W m 2 (Mohr and Taylor, 2000). The value of c u however, is not relevant in colorimetry where 
only the relative spectral distribution of Planck's radiation is used. 

The value of n of air depends on the partial pressure of each constituent of the air 
and is also wavelength dependent, but for standard air (dry air al 15°C and 101 325 Pa, 
containing 0,03 percent by volume of carbon dioxide), it is approximately 1,00028 throughout 
the visible region. This value has been used in photometry and radiometry for a number of 
years (Blevin, 1972), and is confirmed from the latest physical data showing n more precisely 
as a function of wavelength (Cohn et al., 2003). 

Using Equ. E.1 with n - 1,00028, CIE standard illuminant A can be calculated, with 
negligible differences from the published values (1 count or less in the 6th significant digit), by 

i-*Ak, T) 

S A (k) = exV — (E.2) 

L. iA (660nm, T) 

where c 2 = 1,4388 x10" 2 m-K (ITS-90) and 7" = 2854,742 K. This temperature T is the value 
assigned to CIE standard illuminant A in the Planck's equation for standard air. This implies 
that correlated colour temperature of CIE standard illuminant A should be -2855 K, a change 
of -1 K from the previous value (2856 K). However, TC 1-48 did not come to a consensus at 
this time to revise the definition of correlated colour temperature using n = 1,000 28, because 
the form of Pianck's equation in vacuum (n is equal to exactly 1) has been used historically 
and it was concerned that such a revision would cause a small discontinuity from the values 
obtained in the past (though the difference is practically insignificant and matters only in 
rigorous calculations). It was also concerned that the revision still would not describe Planck's 
radiation in air perfectly; the value of n is slightly wavelength dependent, which would bring 
the CIE standard illuminant A deviating very slightly off from a perfect Planckian radiator 
(though the deviation would be less than 0,005% - calculated using data in Cohn et al., 
2003. 

Therefore, in the current recommendation in CIE 15:2004, colour temperature and 
correlated colour temperature are calculated using Equ. E.1 with n-1 (exactly 1), thus no 
change from the previous practice. This recommendation may be subject to change in the future. 

References 

BLEVIN, W.R., 1972. Corrections in Optical Pyrometry and Photometry for the Refractive 
Index of Air. Metrologia, 8, 140-147, 1972. 

COHN, E.R, LIDE, D.R. and TRIGG, G.L., Editors, 2003. AIP Physics Desk Reference. Third 
Edition. Springer-Veriag, 2003. 

MIELENZ, K.D., SAUNDERS, R.D., PARR, A.C. and HSIA, J.J., 1991. The New International 
Temperature Scale of 1990 and its Effect on Radiometric, Photometric, and Colorimetric 
Measurements and Standards, in CIE 91-1991. Proc. of the 22 nd Session of the CIE, D2, 65- 
68,1991 

MOHR, P.J. and TAYLOR, B.N., 2000. CODATA recommended values of the fundamental 
physical constants: 1998. Reviews of Modern Physics, 72/2, 351-495, 2000. 



67 



CiE 15:2004 



PRESTON-THOMAS, H., 1990. The International Temperature Scale of 1990, Metrologia 27, 
3-10, 1990. 

EXPLANATORY COMMENTS 

1 CIE Division 1 (at its meeting in Rochester in 2001) and CIE Division 2 (at its meeting 
in Gaithersburg in 2001) confirmed that wavelengths measured in standard air (dry air 
at 15°C and 101 325 Pa, containing 0,03 percent by volume of carbon dioxide) should 
be used in ail CIE publications. 

2 This recommendation deviates from earlier recommendations regarding CIE sources 
A, B, C (CIE, 1931; CIE, 1951). A distinction is made between illuminant and source. 
The term source refers to a physical emitter of light, such as a lamp or the sun and 
sky. The term illuminant refers to a specific spectral power distribution, not 
necessarily provided directly by a source, and not necessarily realizable as a source. 
The present recommendation first defines illuminants by relative spectral power 
distributions and then sources. The definition of the sources is considered secondary, 
as it is conceivable that new developments in lamps and filters will bring about 
improved sources that represent the illuminants more accurately and are more 
suitable for laboratory use. At present, no recommendation has been made for a 
source representing standard illuminant D65. The original recommendations 
regarding standard illuminant D65 (originally called D 65 ) and other illuminants D 
representing daylight of different correlated colour temperatures are given in CIE 
Proceedings (CIE, 1963; CIE, 1967). 

In 1968 the Comite International des Poids et Mesures modified the "International 
Practical Temperature Scale, 1948 (amended 1960)" and the value of the radiation 
constant c 2 was set equal to 1,4388-10 i2 m-K. This modification has affected the 
colour temperature or correlated colour temperature of the CIE illuminants and 
sources. 

3 Equation 3.1 is equivalent to and can be derived from the expression 

S(X) = 100 M e ^(X,T) I M ej /( 560, 7), (EN.1) 

where 

Me^UT) = Ci ^ [exp(c 2 I XT) - if, (EN.2) 

X is the wavelength (in nanometres), and the ratio c 2 /7~is given by 

c 2 /r= 1,435 x 10 7 /2 848 nm (EN.3) 

Since the numerical value of c^ cancels out of Equ. E.1, this definition of CIE standard 
illuminant A involves no assumptions about the numerical values of d, c 2 , and T other 
than the ratio defined in Equ. E.3. (See CIE 1998c). 

CIE standard illuminant A was originally defined in 1931 as the relative spectral 
power distribution of a Planckian radiator of temperature 

7ciei9 3 i=2 848K, (EN.4) 

the value of the second radiation constant c 2 then being taken as 

c 2 , cie 1931 = 1 ,435 x 10~ 2 m-K. (EN. 5) 

The form of the definition as now printed was carefully chosen to ensure that CIE 
standard illuminant A was defined as a relative spectral power distribution and not as 
a function of temperature; as explained above, the definition of the relative spectral 
power distribution has not changed since 1931 and Equ. 3.1 simply expresses it in a 
general form. 

What has changed is the temperature assigned to this distribution. The value of c 2 
given in Equ. E.5 and used by the CIE in 1931 is different from the respective values, 
c 2 ,its-27 = 14 350 urn-K, c 2J p T s-48 = 14 380 urrvK, and c 2 j PT s-68 = c 2i rrs~9o = 14 388 um-K, 
that were assigned to this constant in the International Temperature Scales of 1927, 



68 



CI E 15:2004 



1948, 1968 and 1990, respectively. Although this has had no effect on the relative 
spectral power distribution of CIE standard iiiuminant A, the correlated colour 
temperatures of sources recommended for laboratory realizations have been 
different, over the years, depending on the values of c 2 used. As may be seen from 
Equ. E.3, the colour temperatures associated with CIE standard iiiuminant A on the 
various international temperature scales referred to above were 7" 2 7 - 2 848 K, T 48 - 
2 854 K, and 7" 68 = T 90 = 2 856 K, respectively. 

Another change over the years has been the explicit decision that the wavelengths in 
Equ.'s 3.1, E.1 and E.2 should be taken as being in standard air despite the fact that 
the equations are derived from the form of Planck's equation in vacuum. The Planck's 
equation requires a refractive index term if the wavelengths refer to a medium other 
than vacuum. Iiiuminant A was originally defined in 1931 as the relative spectral 
distribution of a Planckian radiator but, historically, wavelengths in standard air have 
always been used in photometry and colorimetry. Despite this, CIE/ISO 10526:1991 
and its revision, ISO 10526:1999(E)/CIE S 005-1998, stated that the term A denoted a 
wavelength in vacuum. This was inconsistent with previous CIE publications, but the 
situation was not addressed until recently. CIE Division 1 and Division 2 agreed in 
2001 that all wavelengths used in CIE Publications should be in standard air 
(explanatory comment 1). The current document follows this decision. ISO 
10526:1999/C!E S 005-1998 is also to be revised to reflect this change (CIE S 014-2 
to be published). The use of standard air wavelengths means that the colour 
temperature of iiiuminant A is very slightly different from the values of T used in the 
above equations but the difference is insignificant for ail practical purposes. See 
Appendix E for further information on the use of Planck's equation for standard air. 

It is important to note that the numerical values defined for CIE standard iiiuminant A 
have never changed. The only issues have been the change of temperature scale 
and the use of standard air. The 1 nm tables given in CIE standard S005 and 
reproduced on the CD-ROM accompanying this report are consistent with Equ. 3.1. In 
cases where calculation at 5 nm intervals is found to produce no significant error, the 
data in Table T.1 can be used. 

The rounded values of S(A) for CIE standard iiiuminant A given in Table T.1 show, in 
several instances, small and insignificant discrepancies of one unit in the last decimal 
from corresponding values commonly used in various publications. The values given 
in Table T.1 are the correctly rounded values and agree with those of the standard. 

The correlated colour temperatures are affected by the numerical value of the 
radiation constant c 2 . In accordance with the International Practical Temperature 
Scale, 1948, amended 1960 which was in use at the time when the procedure for 
calculating daylight illuminants was adopted by the CIE, the value of c 2 was equal to 
1,438 x 10" m-K. With this value, the correlated colour temperature of iiiuminant 
D65 is approximately equal to 6500 K. The change of c 2 to the value of 1 ,438 8 x 10" 2 
m-K (International Practical Temperature Scale, 1968) increases the correlated colour 
temperatures of iiiuminant D65 by the factor 1,4388/1,4380. Thus the correlated 
colour temperature increases by approximately 4 K. 

The method required to calculate the values for the relative spectral power 
distributions of illuminants D50, D55, D65, and D75, in Table T.1 is as follows 

1. Multiply the nominal correlated colour temperature (5000 K, 5500 K, 6500 K or 
7500 K) by 1,4388/1,4380. 

2. Calculate x D and y D using the equations given in the text. 

3. Calculate M^ and M 2 using the equations given in the text. 

4. Round M, and M 2 to three decimal places. 

5. Calculate S(A) every 10 nm by S(Z) = S D (A) + M r S^(A) + M?S 2 (X) using values of 
S (A), SiU) and S 2 (Z) from Table T.2. 

6. Interpolate the 10 nm values of S(A) linearly to obtain values a\ intermediate 
wavelengths. 



69 



CIE 15:2004 



This method should also be followed to calculate the relative spectral power 
distribution of illuminants at other nominal correlated colour temperatures. 

6 This recommendation supersedes the original (CIE, 1931) and is in accordance with 
a later agreement (CIE, 1959). 

7 This recommendation has been changed from the original (CIE, 1931) method 
several times, see joint meeting of E-1.3.1, E-1.3.2 and E-1.2 on June 28, 1967 in 
Washington (CIE, 1967). The present version is the result of a major updating, as 
colorimetric practice has shown that more precise definitions of measuring geometry 
are needed. Regarding practical measurements see aiso (CIE, 1998d). 

8 Where single-beam integrating spheres are used, a correction for the reduction of 
sphere efficiency caused by sample absorption is necessary. Without such a 
correction, the instrument will give a non-linear output. The corrected reflectance is 
given by: 

o = R n) 1-p w (A)-(1-y y ) 

S ^'l-^.tl-S^-fs.^)-^))' 

where R(X) is the uncorrected reflectance of the sample referred to the perfect 
reflecting diffuser, p^(X) is the diffuse/diffuse spectral reflectance of the sphere wall, /j- 
is the fractional area of the /th port, f s is the fractional area of the sample port, and 
p T (X) is the reflectance of the reference standard. The above equation assumes idea! 
integrating characteristics for the sphere and that the other ports have zero effective 
reflectance. 

9 These recommendations are based on the originals (CIE, 1931; CIE, 1959; CIE, 
1963). 

The recommendations given in this document regarding the CIE 1931 standard 
colorimetric observer data deviate from the originals in several ways. The CIE 1931 
standard colorimetric observer is now defined by the colour-matching functions x(X), 

y{X), z(X) from 360 nm to 830 nm at 1 nm intervals (see Table 1 in CIE, 1986a). 
From these data the abridged data reproduced in Table T.4. have been derived by 
selecting every fifth value and rounding to six decimal figures. 

10 Colour-matching functions x(X), y(X), z(X) are relative tristimulus values of 
monochromatic radiators of equal radiant power related to a set of reference stimuli 
[X], [Y], [Z]. 

11 The colour-matching functions x(A), y(A), z{X) given in Table T.4 agree closely 
with those defined originally in 1931. Three minor changes have been introduced: at 
X =775 nm the new values of x(X) is 0,000 059 instead of 0,0000; at X = 555 nm 
y(X) is 1,0000 instead of 1,0002; and at X = 740 nm y(X) is 0,000 249 instead of 
0,0003. These changes are considered insignificant in most colorimetric 
computations. From these corrected tables the CIE standard colorimetric observer 
(CIE, 1986a) was determined. 

12 For daylight illuminant D65 2,464 scotopic trolands corresponds to 1 photopic troland 
(see Wyszecki & Stiles, 1982, p. 104). Rod saturation in 9° extrafoveai vision occurs 
at about 2000-5000 scotopic trolands (see Wyszecki & Stiles, 1982, p. 547). Thus rod 
saturation would occur at a photopic light level of between 812-2 029 trolands. 
Working from the Table in Le Grand (1968, p. 106) that takes into account variation of 
pupil size with light level and the Stiles-Crawford effect, this would correspond to 130- 
380 cd/m 2 (kind contribution by J. Pokorny). 

13 These recommendations formalise procedures for practical colorimetric calculations. 

14 CIE 15:2004 states only the facts on abridgement and truncation. A forthcoming 
publication of a tutorial nature will detail the procedures, with examples showing good 
practice. 



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15 This recommendation is based on the original (CIE, 1955) amended in CIE Bulletin 
No. 3, (CIE, 1957). The use of boldface Roman letters as symbols for vector 
notations is another alternative which was added in the first edition of this publication. 
In the present 3rd edition of the document the recommendation to use "Gothic letters" 
has been dropped. 

16 These recommendations are based on those given in supplement No. 2 to the 1st 
edition of this publication (CIE 1978), the publication on "Industrial colour difference 
evaluation" (CIE 1995a) and the publication "Improvement to industrial colour 
difference evaluation" (CIE, 2001a), with some amendments agreed at TC 1-48 and 
TC 1-59 meetings in Veszprem, 2002 and San Diego, 2003. 

17 In June 1967 the CIE coiorimetry committee recommended to the National 
Committees of the CIE a detailed working program for pursuing the problem of colour 
difference calculations (Wyszecki, 1968). Further guidelines were published in 1978 
(Robertson, 1978). The parametric effects in colour difference evaluation were 
summarised in 1993 (CIE, 1993), and an advanced colour difference calculation 
method was published in 1995 (CIE, 1995a). Recent findings are summarized in 
(CIE, 1999a). The currently recommended colour difference formula is described in 
(CIE, 2001a). 

18 Equations (8.7), (8.9) and (8.11) are based on a suggestion by Pauii (1976), 
according to which below L*=8 a linear L*=f(Y) dependence should be followed. In 
CIE 15.2 decimal approximations were used. This brought the break point of Y/Y n = 

\3 1 Tl 1fi ^ 



to 0,008856, and the exact value of -x to 7,787. At the Technical 

116 J 3 ^ 24 j 

Committee TC 1-48 meeting in Veszprem, 2002, the committee agreed that to secure 
the continuity at the break between the two parts of the equations f{Aji A in ), where 

A^- X, A 2 = V, y4 3 = Z, f-=^-| should be written instead of its approximate value of 

1 f i Ifi^ 2 841 

0,008 856, and similarly — x should be used instead of 7,787 in Equ.'s 

3 1,24 J 108 

(8.7), (8.9) and (8.11). 

19 This recommendation is essentially the same as the original (CIE, 1948). 

20 Previous two publications Special metamerism index: Change in iiluminant 
(Supplement No. 1 to 1st edition of CIE 15-1971 (CIE, 1971) and Special metamerism 
index: Change in observer (CIE, 1989) have been combined in this version of CIE 15. 
CIE 80-1989 is, however, still current, and provides more details on the subject. 

21 Table T.6 gives the relative spectral power distributions of 15 FL-illuminants that 
represent 15 different types of fluorescent lamps. 

The FL1 to FL12 group of lamps were also included in 15.2 (there as F1 to F12). The 
further spectra are enumerated by starting with the number 3, reflecting that they 
have been first introduced when elaborating version 3 of CIE 15. Each of the relative 
spectral power distributions in the standard halophosphate ("St-Halo") group (FL3.1- 
3.3) consists of two semi-broadband emissions of antimony and manganese 
activations in a calcium halo-phosphate phosphor. The "DeLuxe" group (FL 3.4-3.6) 
are more or less enhanced in colour rendering properties as compared to the 
"St-Halo" group, usually using multiple phosphors. Relative spectral power 
distributions of the "DeLuxe" group are flatter and have a wider range in the visible 
spectrum than the "St-Halo" group. Relative spectral power distributions of the 
"Three-band" group (FL3.7-3.11) consist mostly of three narrow-band emissions in 
the red, green, and blue wavelength regions. In most cases the narrow-band 
emissions are caused by ternary compositions of rare-earth phosphors. FL3.12-3.14 
represent modern multiband fluorescent lamp spectra. FL3.15 is the spectrum of a 
fluorescent lamp developed commercially to simulate D65, taken from JIS 8716 (JIS, 
1991). 



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22 In many applications high-pressure metal-halide and sodium lamps are gaining in 
importance. Spectra, as reproduced in Table T.7, with colorimetric data shown in 
Table T.9, are representative spectra of these classes of sources and could be used 
for checking colorimetric properties of objects when illuminated with such lamps. 

23 This is a new Section in the document based on CIE 51, first published in 1981 for 
assessing illuminants D55, D65 and D75 (CIE, 1981), and amended in 1999 with a 
technique to assess the quality of D50 illuminants (CIE, 1999b). 

24 The daylight simulators having suitable categories, as assessed by the method in this 
report, can be used to simulate standard illuminants D50, D55, D65and D75for visual 
matching of object-colour samples, and for reproducing the spectral total radiance 
factor of samples for instrumental colorimetry and spectrophotometry; the samples 
may be non-fluorescent or fluorescent. 

The daylight simulators may also be used for the visual appraisal of the colour 
rendering properties of other light sources, though the present method of evaluation 
for daylight simulators does not directly relate to the evaluation of colour rendering 
properties. 

25 This recommendation was published for the first time in the edition 15.2-1986 of this 
publication. 

26 This section has been updated according to the decisions of CIE Division 1 obtained 
at its meeting in Rochester, USA, 2001. 



72